  We present deep imaging of the most distant dwarf discovered by the Dark
Energy Survey, Eridanus II (Eri II). Our Magellan/Megacam stellar photometry
reaches $\sim$$3$ mag deeper than previous work, and allows us to confirm the
presence of a stellar cluster whose position is consistent with Eri II's
center. This makes Eri II, at $M_V=-7.1$, the least luminous galaxy known to
host a (possibly central) cluster. The cluster is partially resolved, and at
$M_V=-3.5$ it accounts for $\sim$$4\%$ of Eri II's luminosity. We derive
updated structural parameters for Eri II, which has a half-light radius of
$\sim$$280$ pc and is elongated ($\epsilon$$\sim$$0.48$), at a measured
distance of $D$$\sim$$370$ kpc. The color-magnitude diagram displays a blue,
extended horizontal branch, as well as a less populated red horizontal branch.
A central concentration of stars brighter than the old main sequence turnoff
hints at a possible intermediate-age ($\sim$$3$ Gyr) population; alternatively,
these sources could be blue straggler stars. A deep Green Bank Telescope
observation of Eri II reveals no associated atomic gas.
