A candidate diffuse stellar substructure was previously reported in the halo of the nearby dwarf starburst galaxy NGC 4449 by Karachentsev et al. We map and analyze this feature using a unique combination of deep integrated-light images from the BlackBird 0.5 m telescope, and high-resolution wide-field images from the 8 m Subaru Telescope, which resolve the nebulosity into a stream of red giant branch stars, and confirm its physical association with NGC 4449. The properties of the stream imply a massive dwarf spheroidal progenitor, which after complete disruption will deposit an amount of stellar mass that is comparable to the existing stellar halo of the main galaxy. The stellar mass ratio between the two galaxies is ~1:50, while the indirectly measured dynamical mass ratio, when including dark matter, may be ~1:10-1:5. This system may thus represent a "stealth" merger, where an infalling satellite galaxy is nearly undetectable by conventional means, yet has a substantial dynamical influence on its host galaxy. This singular discovery also suggests that satellite accretion can play a significant role in building up the stellar halos of low-mass galaxies, and possibly in triggering their starbursts.