Some ALs do allow pets, but it is my opinion that the owner needs to be able to take full responsibility for their care - staff have little enough time to look after the residents without having to clean up after their pets as well.
At my father's ALF they do allow pets within a weight limit which a 5 lb chihuahua would certainly meet. As noted in the earlier response the staff do not provide any care for the animals - no feeding, no walking, no toileting - so you need to take all responsibility for the animal. They also charge for any damage caused by the animal to carpets, floors, etc.