  We report observations of the remnant of Supernova 1987A with the High
Resolution Camera (HRC) onboard the Chandra X-ray Observatory. A direct image
from the HRC resolves the annular structure of the X-ray remnant, confirming
the morphology previously inferred by deconvolution of lower resolution data
from the Advanced CCD Imaging Spectrometer. Detailed spatial modeling shows
that the a thin ring plus a thin shell gives statistically the best description
of the overall remnant structure, and suggests an outer radius 0.96" +/- 0.05"
+/- 0.03" for the X-ray-emitting region, with the two uncertainties
corresponding to the statistical and systematic errors, respectively. This is
very similar to the radius determined by a similar modeling technique for the
radio shell at a comparable epoch, in contrast to previous claims that the
remnant is 10-15% smaller at X-rays than in the radio band. The HRC
observations put a flux limit of 0.010 cts/s (99% confidence level, 0.08-10 keV
range) on any compact source at the remnant center. Assuming the same
foreground neutral hydrogen column density as towards the remnant, this allows
us to rule out an unobscured neutron star with surface temperature T^\infty >
2.5MK observed at infinity, a bright pulsar wind nebula or a magnetar.
