"Chit" is not often used to refer to a specific item in AE. It usually is more abstract meaning something that is a proxy for money, especially those only valid in specific places or communities. However, in certain places, different words have become more common. "Points" are often dollar-for-dollar debits from a prearranged accounts on college campuses to pay for food, laundry, photocopies, and so on. These are encoded on the student's identification card and more convenient than carrying money with you all around. "Cupons" more often refers to physical objects, pieces of paper, that are to be redeemed only for an item stated on them, or a discount on that item. If you hear about "checks [BE ticks]", "punches", or "stamps", these reference the method that cards distributed by businesses are marked. These cards usually offer a free item after a given number have been purchased. This is a way to get the costomer to return to the store, of course.