Employing deep H{alpha} narrowband imagery, we identified and measured the fluxes of 137 small H II regions in the extreme outer disk (R>=R_25_) of the nearly face-on, Sc I galaxy NGC 628. A majority of these H II regions are located in two faint, outer spiral arms visible in H I maps. The faintest H II regions that could be measured have fluxes of only a few times 10^-16^ergs/cm^2^/s, which correspond to luminosities of 10^36^ergs/s, or a fraction of the Orion Nebula luminosity. The most distant object detected is at R~27kpc from the galaxy center. The massive star formation rate, as measured from the azimuthally averaged H{alpha} flux, is consistent with a monotonic decrease as far as R~1.3R_25_ (20kpc), where there is a sharp drop. The Schmidt law for the whole disk of NGC 628 corresponds to a relatively steep power law with n=2.9+/-0.2, but it "fails" below {Sigma}gas<=4M_{sun}_/pc^2^; the index depends strongly on the CO data used. We derived the luminosity function (LF) of 598 H II regions over the whole disk, and we compared the shapes of the cumulative LFs between R>=R_25_ and R<R_25_; the LF of the outer regions is significantly steeper than that of the inner regions.