A dominant, net buyer of a certain asset receives a private signal that is correlated with its mean value. We call this insider a Boesky Insider when the quality of the received signal is such that the future value of the asset can be predicted with certainty. We show that even an infinitesimal probability of a Boesky Insider results in informational inefficiency of prices. Insisting that the equilibrium be continuous in the signal accentuates the inefficiency to the extent that no information is conveyed. The informational inefficiency not withstanding, the regime that allows insider trading can result in greater liquidity and is, in an ex-ante sense, Pareto superior when compared to a regime in which insider trading is banned.