  The multi-wavelength electromagnetic afterglow from the binary neutron star
merger GW170817/GRB170817A has displayed long-term power-law brightening, and
presented challenges to post-merger models of the non-thermal emission. The
most recent radio observations up to 200 days post-merger suggest that the
afterglow has finally peaked and may now be fading, but fading has not been
confirmed in the X-rays. We present new, deep Chandra observations of
GW170817/GRB170817A at 260 days post-merger that reveal an X-ray flux of
F{0.3-8keV} = 1.1 x 10^-14 erg/s/cm^2, and confirm that the X-ray light curve
is now also fading. Through rigorous comparisons to previous Chandra
observations of GW170817/GRB170817A, X-ray fading is detected between 160 and
260 days post-merger at a 4.4 sigma significance, based on the X-ray data
alone. We further constrain the X-ray photon index to steepen by <0.5 at 3.1
sigma significance during this period, which disfavors the passing of the
synchrotron cooling frequency through the X-ray band as the cause of the
observed fading. These observations remain consistent with optically thin
synchrotron afterglow emission. If this afterglow emission arises from a
quasi-spherical mildly relativistic outflow, the X-ray fading suggests that the
outflow is now decelerating. Alternatively, if this afterglow arises from a
successful off-axis structured jet, the X-ray fading suggests that emission
from the jet core has already entered the line of sight.
