Chickens are birds, which are a different group of vertebrates from mammals. Birds lay eggs, while most mammals give birth to live young and nurse them with their mammary glands. The only exceptions to this are the platypus and echidna, which are monotremes, or egg-laying mammals.
In order for an animal to be classified as a mammal it must have hair, as well as fat glands and sweat glands. Female mammals have mammary glands. Mammals give birth to live young and nurse their young. All mammals are vertebrates, and also have several types of teeth.