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.
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