The purpose of this investigation is to understand the causes and implications of centroid distortion in the LORRI instrument on the New Horizons spacecraft. First, an introduction to the New Horizons space program is provided, and the design specifications of the LORRI telescope are discussed. Next, a general theory of perfect imaging is presented, with emphasis on the paraxial equations for the transfer of the chief ray, and the shape of the diffraction-limited point spread function (PSF). Centroid distortion is then defined with respect to these quantities, and methods for quantifying centroid distortion are explained. The nominal LORRI design is analyzed, and the centroid distortion predicted by the nominal design is shown. Astrometric reduction is then performed on a set of twenty in-flight LORRI images, and the actual centroid distortion of the telescope is modeled. Finally, Monte Carlo tolerancing techniques are used to attribute the differences between the predicted centroid distortion and the in-flight centroid distortion to a set of specific manufacturing tolerances.