We report results from Hubble Space Telescope (HST)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 similar to 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 W-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 1 yr 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), color of the cluster sources is identical to that of the field sources, and the mean M-B0 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 that of the field sources.