  We present results from monitoring of the distant (z = 2.64), gravitationally
lensed quasar MG J0414+0534 with the Chandra X-ray Observatory. An Fe Ka line
at 6.49 +/- 0.09 keV (rest-frame) with an equivalent width of ~ 190eV
consistent with fluorescence from a cold medium is detected at the 99 percent
confidence level in the spectrum of the brightest image A. During the last two
observations of our monitoring program we detected a five-fold increase of the
equivalent width of a narrow Fe Ka line in the spectrum of image B but not in
the brighter image A whereas image C is too faint to resolve the line. The
continuum emission component of image B did not follow the sudden enhancement
of the iron line in the last two observations. We propose that the sudden
increase in the iron line strength from ~ 190eV to 900eV only in image B can be
explained with a caustic crossing due to microlensing that selectively enhances
a strip of the line emission region of the accretion disk. The non-enhancement
of the continuum emission in the spectrum of image B suggests that the
continuum emission region is concentrated closer to the center of the accretion
disk than the iron line emission region and the magnification caustic has not
reached close enough to the former region to amplify it. A model of a caustic
crossing event predicts discontinuities in the light-curve of the magnification
and provides an upper limit of ~ 5 x 10^(-4) pc on the outer radius of the Fe
Ka emission region. The non-detection of any relativistic or Doppler shifts of
the iron line in the spectrum of image B implies that the magnification caustic
for the last two observations was located at a radius greater than ~ 100
gravitational radii.
