The gravitational waves emitted in the inspiral of compact binaries are a sensitive probe of the non-linearities of general relativity, and their detection with gravitational-wave interferometers requires the knowledge of the waveform up to high post-Newtonian (PN) order. Using a recent reformulation of the PN expansion which makes use of effective field theory methods, we show that a detection of the gravitational waves emitted in the coalescence of compact binaries can be translated into a measure of the three- and four- graviton vertices of General Relativity. The three-graviton vertex is already constrained from various General Relativity tests, while the four-graviton vertex has never been probed directly. We compute to 1PN order the effect of modified three- and four- graviton vertices on the waveform.