  For the first time, we present a Bayesian time-resolved spectral study of the
X-ray afterglow datasets of GW170817/GRB17017A observed by the Chandra X-ray
Observatory. These include all 12 public datasets, from the earliest
observation taken at $\rm t \sim 9~d$ to the newest observation at $\rm \sim
359~d$ post-merger. While our results are consistent with the other works using
Cash statistic within uncertainty, the Bayesian analysis we performed in this
work have yielded Gaussian-like parameter distributions. We also obtained the
parameter uncertainties directly from their posterior probability
distributions. We are able to confirm that the power-law photon index has
remained constant of $\Gamma \sim 1.6$ throughout the entire year-long
observing period, except for the first dataset observed at $\rm t = 8.9~d$ when
$\Gamma =1.04\pm0.44$ is marginally harder. We also found that the unabsorbed
X-ray flux peaked at $\rm t \sim 155~d$, temporally consistent with the X-ray
flare model suggested recently by Piro et al (2018). The X-ray flux has been
fading since $\sim160$ days after the merger and has returned to the level as
first discovered after one year. Our result shows that the X-ray spectrum of
GW170817/GRB170817A is well-described by a simple power-law originated from
non-thermal slow-cooling synchrotron radiation.
