Chestnuts are found on the medial side of each leg on the forearm of the horse or at the hock of the hind leg. THey are thought to be vestiges of the carpal and tarsal pads of the first digit. They are dark, horny structures found on all equines just like the ergots.

On this picture the chestnut is the white portion on the leg. This is to help you get a good orientation for chestnuts

Close up of a chestnut