  We discuss the X-ray emission observed from Supernova Remnant 1987A with the
Chandra X-ray Observatory. We analyze a high resolution spectrum obtained in
1999 October with the high energy transmission grating (HETG). From this
spectrum we measure the strengths and an average profile of the observed X-ray
lines. We also analyze a high signal-to-noise ratio CCD spectrum obtained in
2000 December. The good statistics (~ 9250 counts) of this spectrum and the
high spatial resolution provided by the telescope allow us to perform
spectroscopic analyses of different regions of the remnant. We discuss the
relevant shock physics that can explain the observed X-ray emission. The X-ray
spectra are well fit by plane parallel shock models with post-shock electron
temperatures of ~ 2.6 keV and ionization ages of ~ 6 x 10^10 cm^3/s. The
combined X-ray line profile has a FWHM of ~ 5000 km/s, indicating a blast wave
speed of ~ 3500 km/s. At this speed, plasma with a mean post-shock temperature
of ~ 17 keV is produced. This is direct evidence for incomplete electron-ion
temperature equilibration behind the shock. Assuming this shock temperature, we
constrain the amount of collisionless electron heating at the shock front at
T_e0 / T_s = 0.11 (+0.02,-0.01). We find that the plasma has low metallicity
(abundances are ~ 0.1 -- 0.4 solar) and is nitrogen enriched (N/O ~ 0.8 by
number), similar to that found for the equatorial ring. Analysis of the spectra
from different regions of the remnant reveals slight differences in the
parameters of the emitting plasma. The plasma is cooler near the optical Spot 1
(at position angle ~ 30 degrees) and in the eastern half of the remnant, where
the bright optical spots are found, than in the western half, consistent with
the presence of slower (~ 500 km/s) shocks entering denser ring material.
