  We used the High Energy Transmission Grating Spectrometer (HETGS) onboard the
Chandra X-ray Observatory to perform two observations, separated by three
weeks, of the Orion Trapezium region. The zeroth order images on the Advanced
CCD Imaging Spectrometer (ACIS) provide spatial resolution of 0.5" and moderate
energy resolution. Within a 160"x140" region around the Orion Trapezium we
resolve 111 X-ray sources with luminosities between 7x10^{28} ergs/s and
2x10^{32} ergs/s. We do not detect any diffuse emission. Many sources appear
much more heavily absorbed, with N_H in the range of 10^22 to 10^23 cm^-2. The
main objective of this paper is to study the Orion Trapezium and its close
vicinity. Most spectra of the very early type members can be fit with a
two-temperature thermal spectrum with a soft component of kT ~ 0.8 keV and a
hard component of kT ~ 2 to 3 keV. We discuss these results in the context of
stellar wind models. We detect eight additional, mostly variable X-ray sources
in the close vicinity of the Trapezium. Five of these X-rays sources are
identified with proplyds and we argue that the X-ray emission originates from
class I, II and III protostars at the cores of the proplyds.
