A measurement of the absolute fluorescence yield of the 337 nm nitrogen band, relevant to ultra-high energy cosmic ray (UHECR) detectors, is reported. Two independent calibrations of the fluorescence emission induced by a 120 GeV proton beam were employed: Cherenkov light from the beam particle and calibrated light from a nitrogen laser. The fluorescence yield in air at a pressure of 1013 hPa and temperature of 293 K was found to be Y 337 = 5.61 +/- 0.06 stat +/- 0.22 syst photons/MeV. When compared to the fluorescence yield currently used by UHECR experiments, this measurement improves the uncertainty by a factor of three, and has a significant impact on the determination of the energy scale of the cosmic ray spectrum.