  We present the results of deep, high-resolution, multi-band optical
observations of the field of the young (~ 5,000 yrs) 16 ms X-ray pulsar PSR
J0537$-$6910 performed with the Advanced Camera for Surveys (ACS) aboard the
Hubble Space Telescope (HST). Although a few new potential counterparts have
been detected within or close to the revised Chandra X-ray error circle (~1
arcsec) of the pulsar, only two of them (with magnitudes m_{814W} ~ 23.9 and
m_{814W} ~ 24.2) show indications of a peculiar spectrum which could be related
to optical emission from the pulsar. This might be true also for a third,
fainter, candidate detected only in one filter (with magnitude m_{814W} ~
26.7). If either of the two brighter candidates is indeed the actual
counterpart, the optical output of PSR J0537-6910 would make it similar to
young Crab-like pulsars. If not, it would mean that PSR J0537-6910 is
significantly underluminous with respect to all pulsars detected in the optical
