An optical frequency comb generated with an electro-optic phase modulator and a chirped radiofrequency waveform is used to perform pump-probe spectroscopy on the D1 and D2 transitions of atomic potassium at 770.1 nm and 766.7 nm, respectively. With a comb tooth spacing of 200 kHz and an optical bandwidth of 2 GHz the hyperfine transitions can be simultaneously observed. Interferograms are recorded in as little as 5 μs (a timescale corresponding to the inverse of the comb tooth spacing). Importantly, the sub-Doppler features can be measured as long as the laser carrier frequency lies within the Doppler profile, thus removing the need for slow scanning or a priori knowledge of the frequencies of the sub-Doppler features. Sub-Doppler optical frequency comb spectroscopy has the potential to dramatically reduce acquisition times and allow for rapid and accurate assignment of complex molecular and atomic spectra which are presently intractable.