  Type II supernovae (SNe) stem from the core collapse of massive ($>8\
M_{\odot}$) stars. Owing to their short lifespan, we expect a very low rate of
such events in elliptical host galaxies, where the star-formation rate is low,
and which mostly consist of an old stellar population. SN 2016hil (iPTF16hil)
is a Type II supernova located in the extreme outskirts of an elliptical galaxy
at redshift $z=0.0608$ (projected distance $27.2$ kpc). It was detected near
peak brightness ($M_{r} \approx -17$ mag) 9 days after the last nondetection.
SN 2016hil has some potentially peculiar properties: while presenting a
characteristic spectrum, the event was unusually short lived and declined by
$\sim 1.5$ mag in $< 40$ days, following an apparently double-peaked light
curve. Its spectra suggest a low metallicity ($Z<0.4\ Z_{\odot}$). We place a
tentative upper limit on the mass of a potential faint host at
$\log(M/M_{\odot}) =7.27^{+0.43}_{-0.24}$ using deep Keck optical imaging. In
light of this, we discuss the possibility of the progenitor forming locally,
and other more exotic formation scenarios such as a merger or common-envelope
evolution causing a time-delayed explosion. Further observations of the
explosion site in the ultraviolet are needed in order to distinguish between
the cases. Regardless of the origin of the transient, observing a population of
such seemingly hostless Type II SNe could have many uses, including an estimate
the number of faint galaxies in a given volume, and tests of the prediction of
a time-delayed population of core-collapse SNe in locations otherwise
unfavorable for the detection of such events.
