We present results from spatially resolved spectral analyses of the northeastern (NE) rim of the Cygnus Loop supernova remnant (SNR) based on two Chandra observations. One pointing includes northern outermost abundance-enhanced regions discovered by recent Suzaku observations, while the other pointing is located on regions with "normal" abundances in the NE rim of the Cygnus Loop. The superior spatial resolving power of Chandra allows us to reveal that the abundance-enhanced region is concentrated in a ~200^'' thickness region behind the shock front. We confirm absolute metal abundances (i.e., relative to H), as well as abundance ratios between metals, are consistent with those of the solar values within a factor of ~2. Also, we find that the emission measure in the region gradually decreases toward the shock front. These features are in contrast with those of the ejecta fragments around the Vela SNR, which leads us to believe that the abundance enhancements are not likely due to metal-rich ejecta. We suggest that the origin of the plasma in this region is the interstellar medium (ISM). In the "normal" abundance regions, we confirm that abundances are depleted to the solar values by a factor of ~5 that is not expected in the ISM around the Cygnus Loop. Introduction of nonthermal emission in our model fitting cannot naturally resolve the abundance-depletion problem. The origin of the depletion still remains as an open question.