We report the discovery of peculiar features in the optical spectrum of 4C+22.25, a flat spectrum radio quasar at z = 0.4183 observed in the Sloan Digital Sky Survey and in a dedicated spectroscopic follow-up from the Nordic Optical Telescope. The Hβ and Hα lines show broad profiles (FWHM ~ 12,000 km s-1), faint fluxes, and extreme offsets (Δv = 8700 ± 1300 km s-1) with respect to the narrow emission lines. These features show no significant variation in a time lag of ~3.1 yr (rest frame). We rule out possible interpretations based on the superposition of two sources or on recoiling black holes, and discuss the virtues and limitations of a massive black hole binary scenario.