From radial velocities determined in high signal-to-noise digital spectra, we report the discovery that the brightest component of the binary system HD 150136 is of spectral type O3. We also present the first double-lined orbital solution for this binary. Our radial velocities confirm the previously published spectroscopic orbital period of 2.6 d. He II absorptions appear double at quadratures, but single lines of N v and N IV visible in our spectra define a radial velocity orbit of higher semi-amplitude for the primary component than do the He II lines. From our orbital analysis, we obtain minimum masses for the binary components of 27 and 18 M⊙. The neutral He absorptions apparently do not follow the orbital motion of any of the binary components, thus they most probably arise in a third star in the system.