  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 deg$^2$ 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 $H_0 = 70$\, km s$^{-1}$ Mpc$^{-1}$) with
the distance of $40 \pm 8$\, Mpc reported by the LIGO Scientific Collaboration
and the Virgo Collaboration (LVC). At detection the transient had magnitudes
$i\approx 17.30$ and $z\approx 17.45$, and thus an absolute magnitude of $M_i =
-15.7$, 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.
