This paper considers competitive search equilibrium in a market for a good whose quality differs across sellers. Each seller knows the quality of the good that he or she is offering for sale, but buyers cannot observe quality directly. We thus have a "market for lemons" with competitive search frictions. In contrast to Akerlof (1970), we prove the existence of a unique equilibrium, which is separating. Higher-quality sellers post higher prices, so price signals quality. The arrival rate of buyers is lower in submarkets with higher prices, but this is less costly for higher-quality sellers given their higher continuation values. For some parameter values, higher-quality sellers post the full-information price; for other values these sellers have to post a higher price to keep lower-quality sellers from mimicking them. In an extension, we show that if sellers compete with auctions, the reserve price can also act as a signal.