  The XMM Cluster Archive Super Survey (X-CLASS) is a serendipitously-detected
X-ray-selected sample of 845 galaxy clusters based on 2774 XMM archival
observations and covering approximately 90 deg$^2$ spread across the
high-Galactic latitude ($|b|>20$ deg) sky. The primary goal of this survey is
to produce a well-selected sample of galaxy clusters on which cosmological
analyses can be performed. This article presents the photometric redshift
followup of a high signal-to-noise subset of 266 of these clusters with
declination $\delta<+20$ deg with GROND, a seven channel ($grizJHK$)
simultaneous imager on the MPG 2.2m telescope at the ESO La Silla Observatory.
We use a newly developed technique based on the red sequence colour-redshift
relation, enhanced with information coming from the X-ray detection to provide
photometric redshifts for this sample. We determine photometric redshifts for
236 clusters, finding a median redshift of $z=0.39$ with an accuracy of $\Delta
z = 0.02 (1+z)$ when compared to a sample of 76 spectroscopically confirmed
clusters. We also compute X-ray luminosities for the entire sample and find a
median bolometric luminosity of $7.2\times10^{43} \mathrm{erg\ s^{-1}}$ and a
median temperature 2.9 keV. We compare our results to the XMM-XCS and XMM-XXL
surveys, finding good agreement in both samples. The X-CLASS catalogue is
available online at http://xmm-lss.in2p3.fr:8080/l4sdb/.
