  We discovered Swope Supernova Survey 2017a (SSS17a) in the LIGO/Virgo
Collaboration (LVC) localization volume of GW170817, the first detected binary
neutron star (BNS) merger, only 10.9 hours after the trigger. No object was
present at the location of SSS17a only a few days earlier, providing a
qualitative spatial and temporal association with GW170817. Here we quantify
this association, finding that SSS17a is almost certainly the counterpart of
GW170817, with the chance of a coincidence being < 9 x 10^-6 (90% confidence).
We arrive at this conclusion by comparing the optical properties of SSS17a to
other known astrophysical transients, finding that SSS17a fades and cools
faster than any other observed transient. For instance, SSS17a fades >5 mag in
g within 7 days of our first data point while all other known transients of
similar luminosity fade by <1 mag during the same time period. Its spectra are
also unique, being mostly featureless, even as it cools. The rarity of
"SSS17a-like" transients combined with the relatively small LVC localization
volume and recent non-detection imply the extremely unlikely chance
coincidence. We find that the volumetric rate of SSS17a-like transients is <
1.6 x 10^4 Gpc^-3 year^-1 and the Milky Way rate is <0.19 per century. A
transient survey designed to discover similar events should be high cadence and
observe in red filters. The LVC will likely detect substantially more BNS
mergers than current optical surveys will independently discover SSS17a-like
transients, however a 1-day cadence survey with LSST could discover an order of
magnitude more events.
