We identify a new cosmological signal, the Doppler-boosted cosmic infrared background (DB CIB), arising from the peculiar motion of the galaxies whose thermal dust emission source the cosmic infrared background (CIB). This new observable is an independent probe of the cosmic velocity field, highly analogous to the well-known kinematic Sunyaev-Zel'dovich (KSZ) effect. Interestingly, DB CIB does not suffer from the "KSZ optical depth degeneracy," making it immune from the complex astrophysics of galaxy formation. We forecast that the DB CIB effect is detectable in the cross-correlation of CCAT-Prime and DESI-like experiments. We show that it also acts as a new CMB foreground which can bias future KSZ cross-correlations, if not properly accounted for.