In a single-item auction, a duplicitous seller may masquerade as one or more bidders in order to manipulate the clearing price. This paper characterizes auction formats that are shill-proof: a profit-maximizing seller has no incentive to submit any shill bids. We distinguish between strong shill-proofness, in which a seller with full knowledge of bidders' valuations can never profit from shilling, and weak shill-proofness, which requires only that the expected equilibrium profit from shilling is nonpositive. The Dutch auction (with suitable reserve) is the unique optimal and strongly shill-proof auction. Moreover, the Dutch auction (with no reserve) is the unique prior-independent auction that is both efficient and weakly shill-proof. While there are a multiplicity of strategy-proof, weakly shill-proof, and optimal auctions; any optimal auction can satisfy only two properties in the set {static, strategy-proof, weakly shill-proof}.