We have identified the optical counterpart of the ULX source P13 in the nearby spiral galaxy NGC 7793. The object is a V ˜ 20.5 mag star, ten times brighter than any other established counterpart of a ULX in nearby galaxies. Medium resolution optical spectroscopy carried out in 2008 and 2009 with the ESO-VLT reveals the presence of narrow high order Balmer, He I and Mg II absorption lines indicating a late B-type supergiant companion star with mass between 10 and 20 M&sun;. Stellar Heta and He II lambda4686 Å emission lines are also seen superposed on the photospheric spectrum. We detect different patterns of radial velocity variations from the emission and absorption lines over a time interval of one month. The velocity of the high order Balmer absorption lines changes by ˜100 km s-1 while the Heta and He II lambda4686 Å emission components vary by about the same amount but with a different phasing. Assuming that the observed velocity changes trace the motion of the mass-donor star and of the X-ray source implies a mass of the accreting black hole in the range of 3 to 100 M&sun; with a most probable value of ˜10 to 20 M&sun;. We expect an orbital period in the range of 20 to 40 days based on the low density of the supergiant star. P13 is likely in a short-lived, and thus rare high X-ray luminosity evolutionary state associated with the ascension of the donor star onto the supergiant stage. Based on optical observations obtained at ESO under programme 084.D.0881(A).