© 2017. The American Astronomical Society. All rights reserved.. 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 broadband UV-through-IR photometry of NGC 4993. The spectrum and broadband spectral-energy distribution indicate that NGC 4993 has a stellar mass of and star formation rate of 0.003 yr-1, 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 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.