  Despite the unique X-ray behavior of the compact bursting X-ray source
MXB1730-335, the "Rapid Burster" (RB) in the highly reddened globular cluster
Liller 1, to date there has been no known optical/IR counterpart for the
object, no precise astrometric solution that correlates X-ray, radio, and
optical positions and thus restricts the number of possible candidates, nor
even published IR images of the field. We solve a previous radio/X-ray
positional discrepancy, presenting the results of precise Chandra X-ray
imaging, which definitively show that the radio source is positionally aligned
with MXB1730-335. At the same time, we have detected three additional low
luminosity (Lx~10e34 erg/s) X-ray sources within two core radii, which are
possibly quiescent low-mass X-ray binaries. We present both ground-based and
Hubble Space Telescope infrared imaging of the field (in quiescent and bursting
X-ray states of the RB), together with the necessary astrometric solution to
overlay the radio/X-ray source positions. Even at HST resolution, the RB field
is very complex and there are multiple candidates. No object of unusual color,
or of substantial variability in quiescent versus active or burst versus
non-burst states, is identified. Further, more sensitive HST/NICMOS and/or
ground-based adaptive-optics observations are needed to confidently identify
the proper counterpart. In the case of the RB, uncertain but plausible
calculations on the effects of the burst on the binary companion indicate that
detection of a variable candidate should be feasible.
