  Cas A is a Galactic supernova remnant whose supernova explosion is observed
to be of Type IIb from spectroscopy of its light echo. Having its SN type
known, observational constraints on the mass-loss history of Cas A's progenitor
can provide crucial information on the final fate of massive stars. In this
paper, we study X-ray characteristics of the shocked ambient gas in Cas A using
the 1 Ms observation carried out with the Chandra X-Ray Observatory and try to
constrain the mass-loss history of the progenitor star. We identify thermal
emission from the shocked ambient gas along the outer boundary of the remnant.
Comparison of measured radial variations of spectroscopic parameters of the
shocked ambient gas to the self-similar solutions of Chevalier show that Cas A
is expanding into a circumstellar wind rather than into a uniform medium. We
estimate a wind density nH ~ 0.9 $\pm$ 0.3 cm$^{-3}$ at the current outer
radius of the remnant (~3 pc), which we interpret as a dense slow wind from a
red supergiant (RSG) star. Our results suggest that the progenitor star of Cas
A had an initial mass around 16 Msun, and its mass before the explosion was
about 5 Msun, with uncertainties of several tens of percent. Furthermore, the
results suggest that, among the mass lost from the progenitor star (~11 Msun),
a significant amount (more than 6 Msun) could have been via its RSG wind.
