Chestnut is one of the three base colors of a horse. These horses have a red coat, mane and tail.
A chestnut horse has to have two copies of the recessive extension gene for their coat to be red (ee) having at least one dominant copy will result in a black coat. Chestnuts don't have black so they can have any mix of dominant and recessive agouti (aa, Aa or AA) since this gene makes the black stick to the points.
Liver chestnut horses have a darker coat.