The muon anomalous magnetic moment has been measured in a new experiment at Brookhaven. Polarized muons were stored in a superferric ring, and the angular frequency difference, ωabetween the spin precession and orbital frequencies was determined by measuring the time distribution of high-energy decay positrons. The ratio R of ωato the Larmor precession frequency of free protons, ωpin the storage-ring magnetic field was measured. We find R = 3.707220(48) × 10-3. With μμ/μp= 3.18334547(47) this gives aμ+= 1165925(15) × 10-9(±13 ppm), in good agreement with the previous CERN measurements for μ+and μ-and of approximately the same precision.