A lowest unique bid auction allocates a good to the agent who submits the lowest bid that is not matched by any other bid. This peculiar auction format is becoming increasingly popular over the Internet. We show that when all the bidders are rational such a selling mechanism can lead to positive profits only if there is a large mismatch between the auctioneer's and the bidders' valuation. On the contrary, the auction becomes highly lucrative if at least some bidders are myopic. In this second case, we analyze the key role played by the existence of some private signals that the seller sends to the bidders about the status of their bids. Data about actual auctions confirm the profitability of the mechanism and the limited rationality of the bidders.