Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration, and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrated an optical phase measurement with an entangled four-photon interference visibility greater than the threshold to beat the standard quantum limit - the limit attainable without entanglement. These results open the way for new high-precision measurement applications.