In gratings, incident light can couple strongly to plasmons propagating through periodically spaced slits in a metal film, resulting in a strong, resonant absorption whose frequency is determined by the nanostructure periodicity. When a grating is patterned on a silicon substrate, the absorption response can be combined with plasmon-induced hot electron photocurrent generation. This yields a photodetector with a strongly resonant, narrowband photocurrent response in the infrared, limited at low frequencies by the Schottky barrier, not the bandgap of silicon. Here we report a grating-based hot electron device with significantly larger photocurrent responsivity than previously reported antenna-based geometries. The grating geometry also enables more than three times narrower spectral response than observed for nanoantenna-based devices. This approach opens up the possibility of plasmonic sensors with direct electrical readout, such as an on-chip surface plasmon resonance detector driven at a single wavelength.