The complexity of the Black-White Pebbling Game has remained an open problem for 30 years. It was devised to capture the power of non-deterministic space bounded computation. Since then it has been continuously studied and applied to problems in diverse areas of computer science including VLSI design and more recently propositional proof complexity. In 1983, determining its complexity was rated as "An Open Problem of the Month" in David Johnson's NP-Completeness Column. In this paper we show that the Black-White Pebbling Game is PSPACE-complete.