  We report results from Hubble Space Telescope WFPC2 imaging of the field of
the luminous, bursting X-ray source in the globular cluster NGC 6441. Although
the X-ray position is known to a precision of a few arcseconds, this source is
only ~6'' from the cluster center, and the field contains hundreds of stars
within the 3'' X-ray error circle, making it difficult to isolate the optical
counterpart. Nevertheless, our multicolor images reveal a single, markedly
UV-excess object with m_{336}=19.0, m_{439}=19.3, within the X-ray error
circle. Correcting for substantial reddening and bandpass differences, we infer
B_0=18.1, (U-B)_0=-1.0, clearly an unusual star for a globular cluster.
Furthermore, we observe an ultraviolet intensity variation of 30% for this
object over 0.5 hr, as well as an even greater variation in m_{439} between two
HST observations taken approximately one year apart. The combination of
considerable UV-excess and significant variability strongly favors this object
as the optical counterpart to the low-mass X-ray binary X1746-370. With a group
of five optical counterparts to high-luminosity globular cluster X-ray sources
now known, we present a homogeneous set of HST photometry on these objects, and
compare their optical properties with those of field low-mass X-ray binaries.
The mean (U-B)_0 color of the cluster sources is identical to that of the field
sources, and the mean M_{B_0} is similar to bursters in the field. However, the
ratio of optical to X-ray flux of cluster sources seems to show a significantly
larger dispersion than field sources.
