Einstein's theory of general relativity (GR) has passed all precision tests to date. At some scale, however, the theory must be reconciled with quantum mechanics in a quantum theory of gravity. Merging binary black holes probe the non-linear, high-curvature, dynamical regime of gravity, and thus observations of these systems with gravitational wave detectors may contain signatures of such a theory. To date, however, LIGO has only performed precise null tests of GR by comparing detector data with full gravitational waveforms generated by numerical relativity in GR. I will talk about our present work to produce numerical relativity binary black hole waveforms in beyond-GR theories, thus allowing for a full test of GR. In particular, I will speak about our work to produce binary black hole waveforms in dynamical Chern-Simons gravity, a beyond-GR theory with motivations in string theory and loop quantum gravity.