No Constitutional Right to Have Pigeons as Pets Here's another issue that Supreme Court nominees may have to study up on. A federal appeals court supports the city of Chicago upholding a ban on keeping pigeons as pets. People who like to race pigeons challenged the law, saying it was unconstitutional. One pigeon racer says the birds are not "bad, dirty and evil," but birds of "pedigree." But the court says Chicago was within its power to ban pets that scatter feathers, leave droppings and coo too much.