We present an analysis of the host-galaxy environment of Swope Supernova Survey 2017a (SSS17a), the discovery of an electromagnetic counterpart to a gravitational wave source, GW170817. SSS17a occurred 1.9 kpc (in projection; 10.2) from the nucleus of NGC 4993, an S0 galaxy at a distance of 40 Mpc. We present a Hubble Space Telescope (HST) pre-trigger image of NGC 4993, Magellan optical spectroscopy of the nucleus of NGC 4993 and the location of SSS17a, and broad-band UV through IR photometry of NGC 4993. The spectrum and broad-band spectral-energy distribution indicate that NGC 4993 has a stellar mass of log (M/M_solar) = 10.49^{+0.08}_{-0.20} and star formation rate of 0.003 M_solar/yr, and the progenitor system of SSS17a likely had an age of >2.8 Gyr. There is no counterpart at the position of SSS17a in the HST pre-trigger image, indicating that the progenitor system had an absolute magnitude M_V > -5.8 mag. We detect dust lanes extending out to almost the position of SSS17a and >100 likely globular clusters associated with NGC 4993. The offset of SSS17a is similar to many short gamma-ray burst offsets, and its progenitor system was likely bound to NGC 4993. The environment of SSS17a is consistent with an old progenitor system such as a binary neutron star system.
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