Webster's on-line dictionary defines a pet as:
a domesticated animal kept for pleasure rather than utility
Congratulations! Get 3 or 4 chickens as young as you can with them still being safe with the cats - for most breeds that would probably be at around 8 weeks of age - from someone who raised them by hand touching and holding them a lot - and then hold them and pet them every day so that they are completely tame, will come when you call them and will hop into your lap and take treats from your hand.
Chickens ARE most definitely domesticated. Parrots are not actually - parrots are never more than a couple of generations from the wild and are acting like they would in the wild - but chickens aren't anything like their ancient ancestors and have been very much reared to live with humans and many breeds are bred specifically to be tame and like handling. You need to have at least three because chickens are very communal in nature. If you get two and one dies the other could die of grief. They really need to have a group which would mean 3 - 4. If you get more than that it will seem like a utilitarian use of the chicken.
I would train the chickens from a young age even to wear a harness and leash. Some people even put chicken diapers on them and bring them indoors!
If you treat your chickens like real pets then if an inspector comes over all you have to do is call to your chickens, pick them up, show the inspector how they like to take walks on a leashes and maybe show them their painted toe nails! lol. Yes, I know someone who paints their chickens' toenails.
Chickens actually make fabulous pets. There are some great chicken forums out there I can send you to - all you would have to do is ask for a consensus as to which breeds would be the best in terms of pet quality along with laying quality and quietness. The best thing would be for no one to even know you have them. Some chicken breeds are really outrageous looking and quite beautiful.
I think you are set. That clause for pets makes it so that you can have a few pet chickens! If anyone asks you if you eat the eggs make sure to say NO! Remember - they are not utilitarian if you aren't raising them for the eggs.
Do you have any children in your family intrigued? If so - it's even easier to train the children with the chickens to show that the chickens are pets for the kids. Even if you don't - many adults keep chickens as pets. I was just outside holding and petting my chickens! They love getting pet under the wings and scratched on the ears and neck.