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The CEO problem is considered when a subset of the agents are under Byzantine attack; that is, they have been taken over and reprogrammed by a malicious intruder. Inner and outer bounds are given for the error exponent with respect to the sum rate, as a function of the fraction of reprogrammed, or traitor, agents. The inner bound is proved by introducing a coding scheme that takes advantage of the fact that the set of honest (non-traitor) agents will report jointly typical information. The CEO looks for a group with the same size as the set of honest agents that appear to do so. Even if not all the agents in this group are honest, the fact that they all agree keeps the probability of error in check. The outer bound is given in two parts, based on two different possible attacks by the traitors. The first is a black hole attack, in which the traitors simply transmit no information at all. The second is one in which they fabricate false data such that the CEO cannot determine which of two possibilities is the truth.