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$$3$ mag deeper than previous work, and allows us to confirm the presence of a stellar cluster whose position is consistent with Eri IIs center. This makes Eri II, at $M_V=-7.1$, the least luminous galaxy known to host a (possibly central) cluster. The cluster is partially resolved, and at $M_V=-3.5$ it accounts for $sim$$4%$ of Eri IIs 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.
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