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he theory of quantum electrodynamics predicts that when a neutron decays to a proton, electron, and antineutrino, that photons can accompany the decay. This radiative decay mode had not been previously measured due to the rarity of detectable photons and the experimental challenges of backgrounds and efficiency. This dissertation discusses the first measurement of the radiative decay mode of the free neutron. The experiment was performed at the National Institute for Standards and Technology in Gaithersburg, MD, by observing the coincidence of an electron, proton, and photon from a neutron decay. The experiment was performed in the bore of a superconducting magnet so that the electron and proton are constrained to cyclotron orbits and guided to a surface barrier detector (SBD) where they are detected. An electrostatic mirror reflected the low energy protons that were initially directed away from the SBD. The mirror voltage was varied to provide discrimination of the signal from backgrounds. To detect the photons, a large area bismuth germanate scintillating crystal was coupled to an avalanche photodiode and operated in the cryogenic, high magnetic field environment. All correlated electron, proton, and photon events were collected as a function of mirror voltage, and the branching ratio was extracted from the data with the aid of a Monte Carlo simulation. The measured branching ratio was (3.09 ± 0.32)x10^-3 for photons with energy from 15 keV to 340 keV. This is consistent with the theoretical prediction of 2.85x10^-3. The dominant uncertainty is the systematic uncertainty of the drift of the photon detector gain during the operation of the experiment. This dissertation describes the experiment, analysis, and final result of this experiment. This dissertation also describes a second run of the experiment that is underway to measure the branching ratio and photon energy spectrum to an uncertainty of 1 %. The centerpiece of this experiment is a 12-element detector to increase the data collection rate and to investigate the systematic uncertainties. The second run will continue to study a fundamental decay process to better understand the neutron decay lifetime.