Mu Columbae is a prototypical weak-wind O star for which we have obtained a high-resolution X-ray spectrum with the Chandra LETG/ACIS instrument and a low-resolution spectrum with Suzaku. This allows us, for the first time, to investigate the role of X-rays on the wind structure in a bona fide weak-wind system and to determine whether there actually is a massive hot wind. The X-ray emission measure indicates that the outflow is an order of magnitude greater than that derived from UV lines and is commensurate with the nominal wind-luminosity relationship for O stars. Therefore, the "weak-wind problem"--identified from cool wind UV/optical spectra--is largely resolved by accounting for the hot wind seen in X-rays. From X-ray line profiles, Doppler shifts, and relative strengths, we find that this weak-wind star is typical of other late O dwarfs. The X-ray spectra do not suggest a magnetically confined plasma-the spectrum is soft and lines are broadened; Suzaku spectra confirm the lack of emission above 2 keV. Nor do the relative line shifts and widths suggest any wind decoupling by ions. The He-like triplets indicate that the bulk of the X-ray emission is formed rather close to the star, within five stellar radii. Our results challenge the idea that some OB stars are "weak-wind" stars that deviate from the standard wind-luminosity relationship. The wind is not weak, but it is hot and its bulk is only detectable in X-rays.