Chickens certainly do have personalities. They „can” make good pets, but not in the sense of litter box trained, etc. I have had some favorites over the many years, and one escpecially likes to follow me around the yard. She would follow me around the garden as I roto-tilled, scratching in the soil. She had absolutely no fear of the noise the tiller made, and would actually get in the way of the tines.
Chickens are social animals and therefore have their „pecking order”. Sometimes they seem to actually be cruel to each other in their way of maintaining that pecking order. Introducing a rooster to a flock of hens brings about other characteristics to the flock. The rooster looks over the hens, and considers the hens as his property. Some roosters can get mean to strangers. If there are 2 roosters in a flock, one will establish himself as the king, and the other always gets chased around.
Personalities seem to be tied to the breed. The brown sex-linked hens are very calm, and would make the best pets. The American breeds of Rhode Island Reds and Barred Rocks are a little more flighty, and would make good pets only if you handled them a lot, and got them used to you. (the more you handle them, the calmer and friendlier they become.)
The Mediteranean type of chickens, like the white leghorns are very very flighty, and I don’t think you could ever make pets of them. They won’t let you come near them without running away from you. Aracanas are also somewhat flighty. But, no matter the breed, they all will look upon you as their „God” who feeds and waters them. If you give them special treats such as table scraps and weeds, they will „worship” you when you approach the run. Chickens really like to have some variety in their diet, and love something out-of-the-ordinary.
I have a special whistle I use whenever I bring them these treats, and as soon as I whistle (from many feet away), they all run at full speed toward the gate of the run to see what I am bringing for them. They will eat right out of my hands. I consider them „pets”, kinda. They know me, and I know them. They respect me, and I respect them. They’re not real big on returning any affection however. But their eggs and organic manure is for me a sort of ”returning affection”.