We report on a search for the host galaxy of FRB 171020, the fast radio burst (FRB) with the smallest recorded dispersion measure (DM; DM = 114 pc cm-3) of our ongoing ASKAP survey. The low DM confines the burst location within a sufficiently small volume to rigorously constrain the identity of the host galaxy. We identify 16 candidate galaxies in the search volume and single out ESO 601-G036, an Sc galaxy at redshift z = 0.00867, as the most likely host galaxy. Ultraviolet and optical imaging and spectroscopy reveal that this galaxy has a star formation rate of approximately 0.1 M o yr-1 and oxygen abundance 12 + log(O/H) = 8.3 ±0.2, properties that are remarkably consistent with the galaxy hosting the repeating FRB 121102. However, in contrast to FRB 121102, follow-up radio observations of ESO 601-G036 show no compact radio emission above a 5σ limit of L 2.1GHz = 3.6 ×1019 W Hz-1. Using radio continuum observations of the field, combined with archival optical imaging data, we find no analog to the persistent radio source associated with FRB 121102 within the localization region of FRB 171020 out to z = 0.06. These results suggest that FRBs are not necessarily associated with a luminous and compact radio continuum source.