  We use archival data of NASA's Chandra X-ray telescope to compile an X-ray
light curve of all four images of the quadruply lensed quasar Q2237+0305
(z=1.695) from January 2006 to January 2007. We fit simulated point spread
functions to the four individual quasar images using Cash's C-statistic to
account for the Poisson nature of the X-ray signal. The quasar images display
strong flux variations up to a factor of ~4 within one month. We can
disentangle the intrinsic quasar variability from flux variations due to
gravitational microlensing by looking at the flux ratios of the individual
quasar images. Doing this, we find evidence for microlensing in image A. In
particular, the time-sequence of the flux ratio A/B in the X-ray regime
correlates with the corresponding sequence in the optical monitoring by OGLE in
the V-band. The amplitudes in the X-ray light curve are larger. For the most
prominent peak, the increase of the X-ray ratio A/B is larger by a factor ~1.6
compared to the signal in the optical. In agreement with theory and other
observations of multiply imaged quasars, this suggests that the X-ray emission
region of this quasar is significantly smaller than the optical emission
region.
