Basenjis being hounds are typically quite prey driven - in my experience. 3 of mine are extremely prey driven, 1 is still a baby so not sure about him yet - but he is more and more interested in rabbits, chipmunks, minks etc. as time passes, and that would be another problem with a small animal.
Mine don't have experience with having small animals around as pets, but I will tell you that 2 of my 4 basenjis can open dog crates (to let a playmate out), and 1 can open doors by turning door knobs, so even if a small animal were caged, it wouldn't be safe in my house. I have heard of many basenjis that can open crates & doors.
Not to make light of the question, but…In my house it would go down something like this: The basenjis are free in the house. 2 minutes later while I'm putting laundry in the machine, basenjis are missing. Liyah opens the door to the chinchilla's room, Liyah, Brando & Ruby would enter. Liyah or Ruby would open the cage, let the chinchilla out, chase it and scare the living daylights out of it and then kill the chinchilla, leave it at the feet of Brando, mom walks into room with dead chinchilla and Brando would take the blame. Ozzy would wonder where everyone went. 
All kidding aside, I think if there were any chance of it working, you would need to start out with a puppy with them together.
In my experience Basenjis brought up with smaller animals cope well but only if the said animals don't run which is the general idea of bringing them up together.
We've had cats, rabbits, ducks, chickens and sheep with our Basenjis. While they were unafraid of each other it worked well, but any animal that flees gets chased and unfortunately in some dreadful instances, killed.
With the sheep my basenjis are fairly controllable (but not off lead) with those who are used to having Basenjis around and just stand and look. Any (which is the majority) who run, get the Basenjis' adrenalin going and the hunting instincts take over.
I also think that were our other animals caged they would have created great interest and the Basenjis would stop at nothing until they were out and running. Make no mistake the Basenji, like most other dogs, is a killer of prey. I know some breeds don't have the same primitive instinct that Basenjis have and it would take much, much more to provoke a kill.
Maya killed my parrot today 
It got out through a window, and to Maya anything outside is fair game so she grabbed it and it was dead in seconds
I have several small animals including rats and hedgehogs and Maya is kept away from them at all times unless very strictly supervised. I wouldnt even leave her loose in a room their cages are in. The times she has been in the room with them out (the hedgehogs), she was absolutely fine and whilst she has shown interest in the rat and parrot cages, she has never attempted to jump on them or anything. But as i found out today, it literally only takes a second for an accident to happen..
Maya, I am so sorry for your loss.
I am sorry Jess! One of the rules in our house is that no pets are allowed to eat each other…we accomplish that by not having any prey species
In seriousness, Ethan keeps asking if we can get a guinea pig, and I just know the dogs would find a way to eat it...or at the very least drive me insane trying to get at it. Soo...yeah, I would be very, VERY reluctant to sell a puppy to someone with small pets. But I suppose it could be done if you had a separate room for the chinchillas...and no kids that might accidentally leave the door open.
As they say, it works till it doesn't…. Basenjis prey on small game... and while they might seem "used" to the critters in the house, as Jess said, only takes one time for an accident to happen.
Jess... so sorry to hear about your Parrot.... since Maya is related to my C-Me, I can totally understand it taking a second... C-Me at 5 months got her first squirrel and at 6 months plucked a bird out of the air that was flying too low!
Oh Jess, I'm so sorry to read about that. I can only imagine how hard it is on you for this to have happened. I hope it doesn't effect your relationship with Maya.
But for the OP, you can see how difficult it can be to have prey/preditors in the same home. I would LOVE to have a pet bunny, but given that I have basenjis, I figured it would not be fair to either species. Perhaps it would be easier to have the prey species first and hope the basenji coming into your home sees the prey as pack not prey, but it only takes a split second for that prey drive to kick in. If you're serious about getting a basenji, I'd suggest having the chins behind 2 doors at all times. so that if one door is left open the basenji still can't get to them. This would be a permanent lifestyle.
This is just a note to say thanks so much for your replies. This is incredibly helpful as we evaluate our options. I really appreciate how helpful every one is.
Even Bs that were raised at commercial breeders, being crated all the time and living in a barn or trailer, can have a high prey drive. My Zippy who was
6 1/2 when rescued would get so excited at the white plastic bag at lure trials. I would practice her by doing an up and back, although usually it was just up.
I know most of my Bs would get excited when visiting petstores that had live animals, even the ones in aquariums. I had to keep them totally away from that area.
My Arnie when he was young had my sister's bird cage tipped and up against the corner walls and that bird was squawking away. I never heard such a racket. He was trying to get to that bird so bad and I was afraid the bird was going to die of fright before I was able to get him away from it.
Jennifer
While my son was in junior high he warted us constantly about getting a guinea pig, and he did not want to accept that with 3 Bs in the household that it was not happening, besides the fact that I hate rat like creatures. After one really bad " warting session" I was stomping out the front door with a momma's threat to lock him in his room forever if I heard the word guinea pig again, I stopped at the door took a deep breath and said, God please HELP me before I "kill' the kid. I opened the door and there on the front step, looking up at me was a 6 inch turtle, I whispered thank you, I can live with a turtle. I called Nathan and he was thrilled, he really wanted a pet in his room. so we had an aquarium, got him a light, and Speedy lived with us until he went to college. Then he allowed his Dad to carry him way out into boonies into a field with a pond to live out his life there. And he was sometimes allowed out with the Bs while we were all in the same room. Since he did not live up to his name of Speedy, after a few sniffs, the Bs pretty much ignored him, but we never left him alone or out of our reach. I would seriously question the wisdom of having a B with small animals in the house and we have lived with them for over 35 years now.
Jess, I am so sorry about your bird. We had a couple of small birds years ago, our basenjis were fine with them so I never even thought twice when a friend brought his male basenji over for a playdate. The lovebird came around the corner and in the blink of an eye the dog had him. It was over in a second, and I cried and grieved for a very long time over that little bird.
Maya may have accepted the parrot in the house, but out on the wing, it became prey. I really am so sorry.
i'm sorry to hear about the bird.
now, as to B's and small animals, i have to fairly say it is up to you, the B,and the small animal in question. i got my boy socialized EARLY with all sorts of small critters. He grew up with rabbits, guinea pigs, birds of all sorts, cats, dogs, and such.
Zumi has never harmed one of my tame rabbits, but has tried to eat some wild ones. He never harmed any of my tame birds, but has tried to eat outside ones, same with cats. Some B's can do fine, ALWAYS supervised of course, and some are hell with small animals. It also depends on the small animal. has it ever been around a dog? how will it react to being sniffed/licked? will your bird flap and screech? will your bunny run? here are some pictures of Zumi with some of my small animals.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/IMG_0787.jpg
Zumi inspecting the Quail cage. he never got to them, and they were kept in a high/B-safe place at all times.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/2Img_0632.jpg
Zumi sniffing a baby bunny. he only ever sniffed them. but they held still, i am sure if one bolted he would have chased. He was raised with rabbits, i generally ran a rabbitry of over 100 rabbits.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0586.jpg
sleeping with the cat. he ADORES cats. would chase then pounce and lick them.. never hurt them.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0567.jpg
Zumi with a pet rat. he could have cared less for them.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0243.jpg
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0244.jpg
Zumi's first meet and greet with a very dog-friendly rabbit. Ben was used to dogs, and was calm, not all small animals are. that's the biggest thing to keep in mind. How will the small animal in question react? and can you keep it safe if your B decides its not friend, but food?
it can go either way. its good to have advise from all sides and experiences.
Some have a larger prey drive than others as well. Misi will kill anything in sight-Sugar will kill birds and rabbits without hesitation. Sugar, Shadow and the puppies are okay with the Ragdoll cat since she doesn't run, but would probably go after something that ran. It really does depend. But then again, I wouldn't trust one completely. And with a Chinchilla? Not a chance, as they are very soft and fluffy and in my experience, a B loves to take apart anything soft and furry. But, if you are going to go with a Basenji, I would definitely start with a puppy and watch, watch, watch, all the time.
I have rats. At first we introduced Hope (basenji) to the ratties. Some of my girls were timid (i have 7) but my leader rat pack girl, Luna, wasnt intimidated by her. They had surpervised "meetings" (Hope basically laid down and Luna tried to run away with her leg.. lol)
In saying this, i still wouldnt trust leaving them in a room together even caged.
My rats have their own room. Where they get to free roam occasionally and live in there 6 story mansions. Hope (basenji) has nothing to do with them and they are always behind closed doors (its only me and the other half at home so we dont have to worry about kids opening the doors etc).
In saying that - i have made sure my cages are secure and sturdy (we made them at home) incase she ever did slip in when we went to go into the rat room. I found that when i had both basenji and rat out together, they were fine. However when Hope watches them when they are caged, she did get stirred up.
So now they are seperated. Hope doesnt take any note in the door they are behind and doesnt even bother tryin to get into that room as she has never had access to it to begin with when we brought her home - its like part of the wall Also - she doesnt see them on display and doesnt get worked up by not being able to get to them as she cant see them. Maybe out of sight, out of mind theory works in this case. - shes not interested unless she sees them
As Tanza says: it works until it doesnt.
Goodluck
Jess I was very sorry to hear about your parrot - you must miss that beautiful bird. As the others say there's always a 'doesn't work' moment.
When we had chickens with iour Basenjis all was well but any flapping did stir up their hunting instinct. I always remember when our ****erel lost his tail because he chose to stretch and flap (showing off to his hens) just as Adonis was walking by. Adonis grabbed his tail and both pulled in opposite directions!!! Hence a 'manx' ****erel!!
Jess, I am so sorry to hear about your parrot - I know they form very close bonds, and the loss must be very hard.
As to Liz's request - IMO, your chinchillas would rank right up there with squirrels and rabbits and your basenji's prey drive might mean no more chincillas pretty quick. Both of mine chase anything smaller than them outside, and even though they have been taught really well by my inside cat that she's a no-no, from time to time Gemma will try to get a nip in - she gets severely hissed at and swatted, so the cat protects herself, but a chinchilla would not do that - and even if it it did, would not cause the B any pain, so personally, I wouldn't chance letting them out of their enclosures if you get a B.
One of the questions on the malinois rescue application was "Do you have any small animals that you wish to keep?"
Hmmmmm . . .
