We have studied the X-ray point-source population of the 30 Doradus (30 Dor) star-forming complex in the Large Magellanic Cloud using high spatial resolution X-ray images and spatially resolved spectra obtained with the Advanced CCD Imaging Spectrometer (ACIS) on board the Chandra X-Ray Observatory. Here we describe the X-ray sources in a 17 0 ; 17 0 field centered on R136, the massive star cluster at the center of the main 30 Dor nebula. We detect 20 of the 32 Wolf-Rayet stars in the ACIS field. The cluster R136 is resolved at the subarcsecond level into almost 100 X-ray sources, including many typical O3-O5 stars, as well as a few bright X-ray sources previously reported. Over 2 orders of magnitude of scatter in L X is seen among R136 O stars, suggesting that X-ray emission in the most massive stars depends critically on the details of wind properties and the binarity of each system, rather than reflecting the widely reported characteristic value L X /L bol ' 10 À7 . Such a canonical ratio may exist for single massive stars in R136, but our data are too shallow to confirm this relationship. Through this and future X-ray studies of 30 Dor, the complete life cycle of a massive stellar cluster can be revealed.