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, ω a, between the spin precession and orbital frequencies was determined by measuring the time distribution of high-energy decay positrons. The ratio R of ω a to the Larmor precession frequency of free protons, ω p, in the storage-ring magnetic field was measured. We find R= 3.707 220 (48)× 10− 3. With μ μ/μ p= 3.183 345 47 (47) this gives a μ+= 1 165 925 (15)× 10− 9 (±13 ppm), in good agreement with the previous CERN measurements for μ+ and μ− and of approximately the same precision.