A very sensitive X-ray investigation of the giant HII region N11 in the LMC was performed using the Chandra X-ray Observatory. The 300ks observation reveals X-ray sources with luminosities down to 10^32 erg/s, increasing by more than a factor of 5 the number of known point sources in the field. Amongst these detections are 13 massive stars (3 compact groups of massive stars, 9 O-stars and one early B-star) with log(Lx/Lbol)~-6.5 to -7, which may suggest that they are highly magnetic or colliding wind systems. On the other hand, the stacked signal for regions corresponding to undetected O-stars yields log(Lx/Lbol)~-7.3, i.e., an emission level comparable to similar Galactic stars despite the lower metallicity. Other point sources coincide with 11 foreground stars, 6 late-B/A stars in N11, and many background objects. This observation also uncovers the extent and detailed spatial properties of the soft, diffuse emission regions but the presence of some hotter plasma in their spectra suggests contamination by the unresolved stellar population.