  Wolf-Rayet (WR) stars are evolved massive stars with strong fast stellar
winds. WR stars in our Galaxy have shown three possible sources of X-ray
emission associated with their winds: shocks in the winds, colliding stellar
winds, and wind-blown bubbles; however, quantitative analyses of observations
are often hampered by uncertainties in distances and heavy foreground
absorption. These problems are mitigated in the Magellanic Clouds (MCs), which
are at known distances and have small foreground and internal extinction. We
have therefore started a survey of X-ray emission associated with WR stars in
the MCs using archival Chandra, ROSAT, and XMM-Newton observations. In the
first paper of this series, we report the results for 70 WR stars in the MCs
using 192 archival Chandra ACIS observations. X-ray emission is detected from
29 WR stars. We have investigated their X-ray spectral properties,
luminosities, and temporal variability. These X-ray sources all have
luminosities greater than a few times 10^32 ergs s^-1, with spectra indicative
of highly absorbed emission from a thin plasma at high temperatures typical of
colliding winds in WR+OB binary systems. Significant X-ray variability with
periods ranging from a few hours up to ~20 days is seen associated with several
WR stars. In most of these cases, the X-ray variability can be linked to the
orbital motion of the WR star in a binary system, further supporting the
colliding wind scenario for the origin of the X-ray emission from these stars.
