  We report the discovery of the faintest known dwarf galaxy satellite of an
LMC stellar-mass host beyond the Local Group, based on deep imaging with
Subaru/Hyper Suprime-Cam. MADCASH J074238+652501-dw lies $\sim$35 kpc in
projection from NGC 2403, a dwarf spiral galaxy at $D$$\approx$3.2 Mpc. This
new dwarf has $M_{g} = -7.4\pm0.4$ and a half-light radius of $168\pm70$ pc, at
the calculated distance of $3.39\pm0.41$ Mpc. The color-magnitude diagram
reveals no evidence of young stellar populations, suggesting that MADCASH
J074238+652501-dw is an old, metal-poor dwarf similar to low luminosity dwarfs
in the Local Group. The lack of either detected HI gas ($M_{\rm HI}/L_{V} <
0.69 M_\odot/L_\odot$, based on Green Bank Telescope observations) or $GALEX$
NUV/FUV flux enhancement is consistent with a lack of young stars. This is the
first result from the MADCASH (Magellanic Analog Dwarf Companions And Stellar
Halos) survey, which is conducting a census of the stellar substructure and
faint satellites in the halos of Local Volume LMC analogs via resolved stellar
populations. Models predict a total of $\sim$4-10 satellites at least as
massive as MADCASH J074238+652501-dw around a host with the mass of NGC 2403,
with 2-3 within our field of view, slightly more than the one such satellite
observed in our footprint.
