We show that every Galileon theory admits a dual formulation as a Galileon theory with new operator coefficients. In n dimensions a free scalar field in Minkowski spacetime is dual to a (n+1)-th order Galileon theory which exhibits the Vainshtein mechanism when coupled to sources and superluminal propagation even on-shell. This demonstrates that superluminal propagation is compatible with an analytic S-matrix and causality. For point sources, the duality interchanges the strongly coupled Vainshtein regime with the weakly coupled asymptotic regime. The duality is made manifest in the context of the decoupling limit of bigravity, but is independent of this.