We report on Chandra observations of the bright ultra-luminous X-ray (ULX) source in NGC3921. Previous XMM observations reported in the literature show the presence of a bright ULX at a 0.5-10 keV luminosity of 2x10^40 erg/s. Our Chandra observation finds the source at a lower luminosity of ~8x10^39 erg/s, furthermore, we provide a Chandra position of the ULX accurate to 0.7" at 90% confidence. The X-ray variability makes it unlikely that the high luminosity is caused by several separate X-ray sources. In 3 epochs of archival Hubble Space Telescope (HST) observations we find a candidate counterpart to the ULX. There is direct evidence for variability between the two epochs of WFPC2 F814W observations with the observation obtained in 2000 showing a brighter source. Furthermore, converting the 1994 F336W and 2000 F300W WFPC2 and the 2010 F336W WFC3 observations to the Johnson U-band filter assuming a spectral type of O7I we find evidence for a brightening of the U-band light in 2000. Using the higher resolution WFC3 observations the candidate counterpart is resolved into two sources of similar color. We discuss the nature of the ULX and the probable association with the optical counterpart(s). Finally, we investigate a potential new explanation for some (bright) ULXs as the decaying stages of flares caused by the tidal disruption of a star by a recoiled supermassive black hole. However, we find that there should be at most only 1 of such systems within z=0.08. ; Comment: 9 pages, 2 figures, accepted for publication in ApJ