The Oak Ridge National Laboratory large liquid-scintillator detector was used in a precise determination of p, the number of neutrons emitted promptly, from spontaneous fission of 252Cf. Measurements of the detector efficiency over a broad energy region were made by means of a proton-recoil technique employing the Oak Ridge Electron Linear Accelerator “white” neutron source. Monte Carlo calculation of the detector efficiency for a spectrum representative of 252Cf fission neutrons was calibrated with these elaborate measurements. The unusually flat response of the neutron detector resulted in elimination of several known sources of error. Experimental measurement was coupled with calculational methods to correct for other known errors. These measurements lead to an unusually small estimated uncertainty of 0.2% in the value obtained, p = 3.773 ± 0.007.