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 similar to 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 MV = -3.5 it accounts for similar to 4% of Eri II's luminosity. We derive updated structural parameters for Eri II, which has a half-light radius of similar to 280 pc and is elongated (epsilon similar to 0.48) at a measured distance of D similar to 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 (similar to 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.