We analyze a mixed oligopoly with free entry by private firms. It is assumed that a state-owned enterprise (SOE) maximizes an increasing function of output, subject to a break-even constraint. We first show that, because of instability, the industry cannot contain more than one SOE. Then we establish an irrelevance result: if the SOE's cost disadvantage relative to private firms is not too large, then aggregate output, aggreagte costs and welfare are the same with and without the SOE. However, for this range of cost disadvantage an SOE monopoly yields higher welfare. Implications for privatization policy are suggested.