Mass transfer in an interacting binary will often strip the mass donor of its entire envelope and spin up the mass gainer to near critical rotation. The nearby B-type star Regulus represents a binary in the post-mass transfer stage: it is a rapid rotator with a very faint companion in a 40 d orbit. Here we present the results of a search for the spectral features of the stripped-down star in an extensive set of high S/N and high resolution spectra obtained with the CFHT/ESPaDOnS and TBL/NARVAL spectrographs. We first determine revised orbital elements in order to set accurate estimates of the orbital Doppler shifts at the times of observation. We then calculate cross-correlation functions of the observed and model spectra, and we search for evidence of the companion signal in the residuals after removal of the strong primary component. We detect a weak peak in the co-added residuals that has the properties expected for a faint pre-white dwarf. We use the dependence of the peak height and width on assumed secondary velocity semiamplitude to derive the semiamplitude, which yields masses of $M_1/M_odot = 3.7 pm 1.4$ and $M_2/M_odot = 0.31 pm 0.10$ (assuming orbital inclination equals the spin inclination of Regulus). We estimate the pre-white dwarf temperature $T_{rm eff} = (20 pm 4)$~kK through tests with differing temperature model spectra, and we find the radius $R_2/R_odot = 0.061 pm 0.011$ from the component temperatures and the flux ratio associated with the amplitude of the signal in the cross-correlation residuals.