Fishbone-type oscillations with poloidal and toroidal mode numbers m = 1, n = 1 have been observed during lower hybrid current drive (LHCD) in the Alcator C-Mod tokamak. At relatively high plasma density and collisionality, the driving mechanism appears to be the nonresonant destabilization of an m/n = 1/1 MHD resistive internal kink mode by the pressure of the suprathermal electrons produced by the LHCD rather than a wave-particle resonance between the mode and the fast electrons. Direct measurements of the fast electrons are consistent with nonresonant destabilization and saturation. The effects of the 1/1 mode kink displacement on the LHCD deposition and fast electron concentration lead to nonresonant saturation mechanisms that may also contribute to the saturation of resonant lower hybrid fishbones.