Technically speaking, chickens and other birds are reptiles. Chickens are very remotely related to mammals, as mammals are descended from creatures that went down a separate evolutionary pathway from the ancestors of birds starting about 320 million years ago.
Based on fossil evidence, chickens and other birds belong to a group of ancient reptiles called the maniraptors. Maniraptors were two-legged, feathery dinosaurs that had evolved a special wrist bone that allowed for powerful movement of the front limbs. In birds, this movement powers flight.
Older scientific classification schemes did not recognize birds as reptiles because reptiles are defined as cold-blooded creatures with scales, while birds are warm-blooded. Despite these differences, birds also share many features with living reptile groups, including the ability to lay eggs. Birds are more closely related to crocodiles than they are to any other animal group alive today.