We present two epochs of near-infrared spectroscopy of the candidate red supergiant counterpart to RX~J004722.4-252051, a ULX in NGC 253. We measure radial velocities of the object and its approximate spectral type by cross-correlating our spectra with those of known red supergiants. Our VLT/X-shooter spectrum is best matched by that of early M-type supergiants, confirming the red supergiant nature of the candidate counterpart. The radial velocity of the spectrum, taken on 2014, August 23, is $417 ± 4$ km/s. This is consistent with the radial velocity measured in our spectrum taken with Magellan/MMIRS on 2013, June 28, of $410 ± 70$ km/s, although the large error on the latter implies that a radial velocity shift expected for a black hole of tens of $M_⊙$ can easily be hidden. Using nebular emission lines we find that the radial velocity due to the rotation of NGC 253 is 351 $±$ 4 km/s at the position of the ULX. Thus the radial velocity of the counterpart confirms that the source is located in NGC 253, but also shows an offset with respect to the local bulk motion of the galaxy of 66 $±$ 6 km/s. We argue that the most likely origin for this displacement lies either in a SN kick, requiring a system containing a $\gtrsim 50$ $M_⊙$ black hole, and/or in orbital radial velocity variations in the ULX binary system, requiring a $\gtrsim 100$ $M_⊙$ black hole. We therefore conclude that RX~J004722.4-252051 is a strong candidate for a ULX containing a massive stellar black hole. ; Comment: 10 pages, 7 figures, accepted for publication in MNRAS