Chickens do mate, in the sense that they engage in sexual copulation, although the anatomical details are different from mating in humans and other animals. Chickens, like many other birds, lack penises, so no penetration occurs during sex. Instead, mating chickens press their sexual organs together to transfer sperm.
A chicken has the same kind of sexual organ whether it is a rooster or hen: the cloaca, a triple-purpose orifice that deals with reproduction as well as expelling liquid and solid waste. Roosters perform a mating dance around a female to initiate courtship. If the female is receptive, the rooster grips the hen's back and head to position their cloacas against one another. The female retains the sperm until an egg cell is released. This usually takes a day. Once the egg is released, it is fertilized by the sperm and the egg is laid after another 24 hours. Mating season is typically in spring and summer, both in the wild and in domesticated chickens.