An optical transition radiation monitor has been developed for the proton beam-line of the T2K long base-line neutrino oscillation experiment. The monitor operates in the highly radioactive environment in proximity to the T2K target. It uses optical transition radiation, the light emitted from a thin metallic foil when the charged beam passes through it, to form a two-dimensional image of the 30 GeV proton beam profile in the transverse plane. One of its key features is an optical system capable of transporting the light over a large distance out of the harsh environment near the target to a lower radiation area where it is possible to operate a camera to capture this light. The monitor measures the proton beam position and width with an accuracy better than 0.5 mm, meeting the physics requirements of the T2K experiment.