Abstract.  We constrain dRGT massive gravity by a causality analysis, which eliminates one of its parameters.  First, we demonstrate that the theory admits a class of exact vacuum solutions: pp-wave spacetimes with a null Killing vector.  Linear fluctuations on these backgrounds do obey the necessary constraints as expected.  However, the longitudinal modes generically undergo a measurable time advance upon crossing, for example, a "sandwich wave" of compact support.  Taking place well within the validity regime of the effective theory, this potentially leads to closed time-like curves.  Our results corroborate the fact that the absence of unphysical modes is not a sufficient consistency condition.  The remedy is to fix a parameter of the theory to a value that rules out the minimal model and, when combined with other constrains derived from unitarity and analyticity of scattering amplitudes, leaves room only for a tiny line segment in the parameter space.