We present 12CO J=1-0 observations from the Caltech Millimeter Array of a field in the nearby spiral galaxy M81. We detect emission from three features that are the size of large giant molecular clouds (GMCs) in the Milky Way Galaxy and M31, but are larger than any known in M33 or the SMC. The M81 clouds have diameters approximately 100 pc and molecular masses 3 * 10^5 solar masses. These are the first GMCs to be detected in such an early type galaxy (Sab) or in a normal galaxy outside the Local Group. The clouds we have detected do not obey the size-linewidth relation obeyed by GMCs in our Galaxy and in M33, and some of them may be GMC complexes that contain several small GMCs. One of these does show signs of sub-structure, and is shaped like a ring section with three separate peaks. At the center of this ring section lies a giant HII region, which may be associated with the molecular clouds.
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