  The Chandra X-ray Observatory (CXO) imaged the high-mass gamma-ray binary
(HMGB) HESS J0632+057 with the Advanced CCD Imaging Spectrometer (ACIS). We
analyzed the CXO data together with 967 ks of archival Swift-XRT observations.
On arcsecond scales we find a hint of asymmetric extended emission. On
arcminute scales, a region of extended emission ("the blob"), located
$\sim$5.5' east of the binary, is seen in both the CXO-ACIS and the Swift-XRT
images. The blob does not have a counterpart in the radio, NIR, IR, or optical
images. The ACIS spectrum of the blob fits either an absorbed power-law model
with photon index $\Gamma\simeq2.6$, or a thermal plasma model with $kT\simeq3$
keV. Since the blob's absorbing column, $N_{\rm H}$, is significantly larger
than that of the binary we conclude that the blob and binary are not directly
related. The somewhat larger very deep XRT image suggests that the binary may
be located within a shell (or cavity). The four ACIS spectra taken within the
$\sim$20 day interval near the light curve minimum suggests that the $N_{\rm
H}$ is varying on timescales of days, possibly due to the inhomogeneous
circumbinary environment. The XRT spectra extracted from the wider orbital
phase intervals support significant changes in $N_{\rm H}$ near the light curve
maximum/minimum, which may be responsible for the substantial systematic
residuals seen near 1 keV, and provide tentative evidence for a Fe line at 6.4
keV. We find no significant periodic signal in the ACIS data up to 0.156 Hz.
