  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.
