Well-behaved infinite signaling games may have no sequential equilibria. The author proves that adding cheap talk to these games 'solves' the nonexistence problem: the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap-talk extension of the limit game. In addition, when the signaling space has no isolated points, any cheap-talk sequential equilibrium outcome can be approximated by a sequential [epsilon]-equilibrium of the game without cheap talk. Copyright 1996 by The Econometric Society.