  We have studied the X-ray point source population of the 30 Doradus
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) aboard the Chandra X-ray
Observatory. Here we describe the X-ray sources in a 17' x 17' 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. 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 two
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 binarity of each system, rather than reflecting the
widely-reported characteristic value L_X/L_bol ~ 10^{-7}. 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
Doradus, the complete life cycle of a massive stellar cluster can be revealed.
