The 1.2 m telescope at the Center for Astrophysics is being used to carry out the first complete CO survey of M31. To date, the entire galaxy out to a radius of at least 15 kpc —- well beyond the optical disk and H I ring — has been observed every half-beamwidth (4.5'), with ∼1 hr of integration per point yielding an rms of 20 mK in 1.3 km s—1 channels. Like H I and other Population I tracers, molecular clouds in M31 are mainly concentrated in a broad ring with a radius of ∼10 kpc, but beyond the peak of the ring molecular gas falls off more sharply than atomic gas. On the assumption of a standard Galactic value for the conversion of CO emission to H2 mass, the average molecular surface density at the peak of the ring is ∼1 M⊙ pc-2 and the total molecular mass of M31 is ∼3 × 108 M⊙. The survey will be essentially repeated during the coming year to improve the signal-to-noise.