Multi-unit auctions are sometimes plagued by the so-called exposure problem. In this paper, we analyze a simple game called the `chopstick auction' in which bidders are confronted with the exposure problem. We analyze the chopstick auction with incomplete information both in theory and in a laboratory experiment. In theory, the chopstick auction has an efficient equilibrium and is revenue equivalent with the second-price sealed-bid auction in which the exposure problem is not present. In the experiment, however, we find that the chopstick auction is slightly less efficient but yields far more revenue than the second-price sealed-bid auction.