We report on the results of our monitoring program of the remnant of SN 1987A with the Advanced CCD Imaging Spectrometer ( ACIS ) on board the Chandra X-ray Observatory . Two new observations have been performed in AO2 , bringing the total to four monitoring observations over the past two years . Over this time period , new techniques for correction of “ Charge Transfer Inefficiency ( CTI ) ” and for use of charge spreading to provide angular resolution somewhat better than the pixel size of the CCD detector have become available at Penn State . We have processed all four observations using sub-pixel resolution to obtain the highest possible angular resolution , and using our CTI correction software to provide more reliable spectral analysis and flux estimations . The high angular resolution images indicate that the X-ray bright knots are convincingly correlated with the optical spots , primarily at \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 1 keV , while higher energy photons are very well correlated with radio images . Our data also provide marginal evidence for radial expansion of the X-ray remnant at a rate of 5200 \pm 2100 km s ^ { -1 } . The X-ray flux appears to linearly increase by \sim 60 % over the 18 month period of these observations . The spectrum is dominated by broad complexes of atomic emission lines and can be fit with a simple model of a plane-parallel shock with electron temperatures of kT \sim 2 - 4 keV and a postshock electron density of n _ { e } \sim 210 - 420 cm ^ { -3 } . The implied 0.5 - 10 keV band luminosity in 2001 April is \sim 1.3 \times 10 ^ { 35 } ergs s ^ { -1 } ; as of that date , we still observe no direct evidence for the central point source , with an upper limit on the observed luminosity of L _ { X } \sim 5.5 \times 10 ^ { 33 } ergs s ^ { -1 } in the 2 - 10 keV band .