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
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
, the least luminous galaxy known to host a (possibly central) cluster. The cluster is partially resolved, and at
it accounts for
of Eri II's luminosity. We derive updated structural parameters for Eri II, which has a half-light radius of
280 pc and is elongated (
0.48), at a measured distance of
D370 kpc. The color-magnitude diagram displays a blue, extended horizontal branch, as well as a less populated red horizontal branch. The presence of the latter, together with a central concentration of stars brighter than the old main sequence turnoff, hints at a possible intermediate-age (
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.