Cheapside and Eastcheap are two streets in the City of London. Cheap is an adjective these days, but originally, in Old English, cheap was a noun. It meant 'bargaining, barter, or exchange of commodities', and could also refer to the place of buying or selling, or the market, which is why the streets have these names. Cheap is a cognate of the German kaufen, to buy.
The adjective cheap is not found before the 16th century, says the OED. It is, in fact, a short form of the earlier good cheap; better cheap and best cheap were common, too. So something that was good cheap in the 14th century was a bargain. The original meaning of the verb to cheapen (16th century) was 'to bargain' or 'ask the price of'. Chapman is mostly known as a surname now, but it is related to cheap its original meaning was 'dealer' or 'tradesman'.