  We report on pointed X-ray observations of IC 10, NGC 147 and NGC 185 made
with the ROSAT High Resolution Imager (HRI). These are three Local Group
galaxies that have never been previously studied in detail in the X-ray regime.
IC 10 is the closest starburst galaxy to our own Galaxy, and NGC 147 and NGC
185 are companions to M31. We have discovered a variable X-ray source
coincident with IC 10. The source is located near the centre of a large,
non-thermal bubble of radio emission, and it is positionally coincident with an
emission line star in IC 10 which has been classified as a WN type Wolf-Rayet
star. We demonstrate that a confusing foreground or background source is
improbable. The X-ray source is probably an X-ray binary in IC 10, and it may
be a Wolf-Rayet + black hole binary. The source has mean and maximum 0.1--2.5
keV isotropic luminosities of about 2 and 4 times 10^{38} erg/s. We do not
detect any sources in the central regions of NGC 147 or NGC 185. We place upper
limits on their central X-ray emission, and we list all X-ray sources
coincident with their outer extents. We also present the first X-ray detections
of the well-studied Algol-type binary TV Cas and the W UMa-type binary BH Cas,
which were both serendipitously observed during our IC 10 pointing.
