No chicken lays a true red egg. The closest thing to red is probably either the terra cotta colored eggs that some Marans lay, or else the pale pink eggs that some Easter Eggers lay. Some people are under the misconception that Cherry Eggers lay red eggs because of their name, but Cherry Eggers are hybrids produced by crossing breeds with reddish feathers (RIR, NHR) and the name refers not to the color of their eggs, but to the reddish color of their feathers.
Welsummers like Marans are well known for their very dark brown eggs (other breeds that are as well are Barnevelders, Empordanesas, and Pendesencas. Sometimes their dark brown eggs will have a slight reddish tint to them, hence the terra cota eggs. All of these breeds can be used for crossing with blue egg laying Ameraucanas to produce Olive Eggers, which lay dark green (olive) colored eggs.