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 \pm 0.4 and a half-light radius of 168 \pm 70 pc , at the calculated distance of 3.39 \pm 0.41 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 H I gas ( M _ { 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 .