We present the Dark Energy Camera (DECam) discovery of the optical counterpart of the first binary neutron star merger detected through gravitational wave emission, GW170817. Our observations commenced 10.5 hours post-merger, as soon as the localization region became accessible from Chile. We imaged 70 deg2 in the i and z bands, covering 93% of the initial integrated localization probability, to a depth necessary to identify likely optical counterparts (e.g., a kilonova). At 11.4 hours post-merger we detected a bright optical transient located 10.6′′ from the nucleus of NGC 4993 at redshift z = 0.0098, consistent (for H0=70\, km s−1 Mpc−1) with the distance of 40±8 Mpc reported by the LIGO Scientific Collaboration and the Virgo Collaboration (LVC). At detection the transient had magnitudes i ≈ 17.30 and z ≈ 17.45, and thus an absolute magnitude of Mi = −15.7, in the luminosity range expected for a kilonova. We identified 1,500 potential transient candidates. Applying simple selection criteria aimed at rejecting background events such as supernovae, we find the transient associated with NGC 4993 as the only remaining plausible counterpart, and reject chance coincidence at the 99.5% confidence level. We therefore conclude that the optical counterpart we have identified near NGC 4993 is associated with GW170817. This discovery ushers in the era of multi-messenger astronomy with gravitational waves, and demonstrates the power of DECam to identify the optical counterparts of gravitational-wave sources.