The first detection of gravitational waves from the binary neutron star merger GW170817 by the LIGO-Virgo Collaboration has provided fundamental new insights into the astrophysical site for r-process nucleosynthesis and on the nature of dense neutron-star matter. The detected gravitational wave signal depends upon the tidal distortion of the neutron stars as they approach merger. We report on relativistic numerical simulations of the approach to binary merger in the conformally flat, quasi-circular orbit approximation. We show that this event serves as a calibration to the quasi-circular approximation and a confirmation of the validity of the conformally flat approximation to the three-metric. We then examine how the detected chirp depends upon the adopted equation of state. This establishes a new efficient means to constrain the nuclear equation of state in binary neutron star mergers.