  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 $417 \pm 4$ km/s. This
is consistent with the radial velocity measured in our spectrum taken with
Magellan/MMIRS on 2013, June 28, of $410 \pm 70$ km/s, although the large error
on the latter implies that a radial velocity shift expected for a black hole of
tens of $M_\odot$ can easily be hidden. Using nebular emission lines we find
that the radial velocity due to the rotation of NGC 253 is 351 $\pm$ 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 $\pm$ 6 km/s. We argue that the most
likely origin for this displacement lies either in a SN kick, requiring a
system containing a $\gtrsim 50$ $M_\odot$ black hole, and/or in orbital radial
velocity variations in the ULX binary system, requiring a $\gtrsim 100$
$M_\odot$ black hole. We therefore conclude that RX~J004722.4-252051 is a
strong candidate for a ULX containing a massive stellar black hole.
