We report on a search for the host galaxy of FRB171020, the fast radio burst with the smallest recorded dispersion measure (DM $=114$ pc cm$^{-3}$) of our on-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, a Sc galaxy at redshift $z=0.00867$, as the most likely host galaxy. UV and optical imaging and spectroscopy reveal this galaxy has a star-formation rate of approximately 0.1 M$_odot$ yr$^{-1}$ and oxygen abundance $12 + log({rm O/H}) = 8.3 pm 0.2$, properties remarkably consistent with the galaxy hosting the repeating FRB121102. However, in contrast to FRB121102, follow-up radio observations of ESO 601-G036 show no compact radio emission above a 5$sigma$ limit of $L_{2.1{rm GHz}}=3.6times 10^{19}$ 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 FRB121102 within the localization region of FRB171020 out to $z=0.06$. These results suggest that FRBs are not necessarily associated with a luminous and compact radio continuum source.
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