We consider a robust analog of the planted clique problem. In this analog, a set S of vertices is chosen and all edges in S are included; then, edges between S and the rest of the graph are included with probability 2 1 , while edges not touching S are allowed to vary arbitrarily. For this semi-random model, we show that the information-theoretic threshold for recovery is ( n ) , in sharp contrast to the classical information-theoretic threshold of ( log ( n )) . This matches the conjectured computational threshold for the classical planted clique problem, and thus raises the intriguing possibility that, once we require robustness, there is no computational-statistical gap for planted clique.