The city says "Dog Registration Information: Registering your dog can be done at any City Clerk office location or online. By Municipal Code 7-12-140, all dogs four months and older must be registered with the City of Chicago."
Cost to Register Your Dog
Unsterilized dog fees are higher because thousands of dogs are euthanized annually or suffer as strays because of unwanted, unplanned litters that could have been prevented by spaying or neutering. One unspayed female and her offspring can produce 67,000 puppies in just six years. Also, sterilized dogs are healthier and have fewer medical problems. In addition, spaying and neutering can make pets less likely to run away or fight with other animals. Other pets (cats, birds, snakes, etc.) are not subject to city licensing.
Dogs must have a current rabies vaccination. Your dog registration expires one year after the date of your dog’s rabies vaccination. Registrations are sold in 1 year or 3 year increments (to coincide with rabies vaccinations).
(Source: City Clerks Office Chicago)
If you want to register your dog visit:Chicago City Clerk's Office