  We have obtained optical and near-infrared images of the field of the
accreting millisecond X-ray pulsar XTE J1751-305. There are no stars in the
0.7'' error circle (0.7'' is the overall uncertainty arising from tying the
optical and X-ray images and from the intrinsic uncertainty in the Chandra
X-ray astrometric solution). We derive limiting magnitudes for the counterpart
of R>23.1, I>21.6, Z>20.6, J>19.6, K>19.2. We compare these upper limits with
the magnitudes one would expect for simple models for the possible donor stars
and the accretion disk subject to the reddening observed in X-rays for XTE
J1751-305 and when put at the distance of the Galactic Centre (8.5 kpc). We
conclude that our non-detection does not constrain any of the models for the
accretion disk or possible donor stars. Deep, near-infrared images obtained
during quiescence will, however, constrain possible models for the donor stars
in this ultra-compact system.
