  We show that the cumulative CO emission from galaxies throughout cosmic
history distorts the spectrum of the cosmic microwave background (CMB) at a
level that is well above the detection limit of future instruments, such as the
Primordial Inflation Explorer (PIXIE). The modeled CO signal has a prominent
bump in the frequency interval 100-200 GHz, with a characteristic peak
intensity of ~ 2$\times$10$^{-23}$ W m$^{-2}$ Hz$^{-1}$ sr$^{-1}$. Most of the
CO foreground originates from modest redshifts, z ~ 2-5, and needs to be
efficiently removed for more subtle distortions from the earlier universe to be
detected.
