  The Eastern Banded Structure (EBS) and Hydra~I halo overdensity are very
nearby (d $\sim$ 10 kpc) objects discovered in SDSS data. Previous studies of
the region have shown that EBS and Hydra I are spatially coincident, cold
structures at the same distance, suggesting that Hydra I may be the EBS's
progenitor. We combine new wide-field DECam imaging and MMT/Hectochelle
spectroscopic observations of Hydra I with SDSS archival spectroscopic
observations to quantify Hydra I's present-day chemodynamical properties, and
to infer whether it originated as a star cluster or dwarf galaxy. While
previous work using shallow SDSS imaging assumed a standard old, metal-poor
stellar population, our deeper DECam imaging reveals that Hydra~I has a thin,
well-defined main sequence turnoff of intermediate age ($\sim 5-6$ Gyr) and
metallicity ([Fe/H] = $-0.9$ dex). We measure statistically significant spreads
in both the iron and alpha-element abundances of $\sigma_{[Fe/H]} = 0.13 \pm
0.02$ dex and $\sigma_{[\alpha/{\rm Fe}]} = 0.09 \pm 0.03$ dex, respectively,
and place upper limits on both the rotation and its proper motion. Hydra~I's
intermediate age and [Fe/H] -- as well as its low [$\alpha$/Fe], apparent
[Fe/H] spread, and present-day low luminosity -- suggest that its progenitor
was a dwarf galaxy, which subsequently lost more than $99.99\%$ of its stellar
mass.
