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 (zQ= 1.695) from 2006 January to 2007 January. We fit simulated point spread functions to the four individual quasar images using Cash's C-statistic to account for the Poissonian 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 of ∼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.