  The mini Broad Absorption Line (BAL) quasar RX J0911.4+0551 was observed with
the Advanced CCD Imaging Spectrometer (ACIS) of the Chandra X-ray Observatory
for ~ 29 ks as part of a gravitational lens (GL) survey aimed at measuring
time-delays. Timing analysis of the light-curve of the lensed image A2 shows a
rapid flux variation with a duration of about 2000s. A Kolmogorov-Smirnov test
shows that the probability that a constant-intensity source would produce the
observed variability is less than ~ 0.2 percent. We discuss possible origins
for the observed short-term X-ray variability. Our gravitational lens models
for the RX J0911.4+0551 GL system predict a time-delay of less than a day
between images A1 and A2. The rapid variability combined with the predicted
short-time delay make RX J0911.4+0551 an ideal system to apply the GL method
for estimating the Hubble constant. We describe the prospects of measuring H_0
within single X-ray observations of GL systems with relatively short time
delays. Modeling of the spectrum of the mini-BAL quasar RX J0911.4+0551
suggests the presence of an intrinsic absorber. Partial covering models are
slightly preferred over models that contain absorption due to intrinsic ionized
or neutral gas.
