  We report subarcsec-resolution X-ray imaging of the core of the Perseus
cluster around the galaxy NGC 1275 with the Chandra X-ray Observatory. The
ROSAT-discovered holes associated with the radio lobes have X-ray bright rims
which are cooler than the surrounding gas and not due to shocks. The holes
themselves may contain some hotter gas. We map strong photoelectric absorption
across the Northern lobe and rim due to a small infalling irregular galaxy,
known as the high velocity system. Two outer holes, one of which was previously
known, are identified with recently found spurs of low-frequency radio
emission. The spiral appearance of the X-ray cooler gas and the outer optical
parts of NGC 1275 may be due to angular momentum in the cooling flow.
