The Liquid Xenon Gamma-Ray Imaging Telescope (LXeGRIT) is the first realization of a liquid xenon time projection chamber for Compton imaging of MeV gamma-ray sources in astrophysics. By measuring the energy deposit and the three spatial coordinates of individual gamma-ray scattering points, the location of the source in the sky is inferred with Compton kinematics reconstruction. The angular resolution is determined by the detectors energy and spatial resolutions, as well as by the separation in space between the first and second scattering. The imaging response of LXeGRIT was established with gamma-rays from radioactive sources, during calibration and integration at the Columbia Astrophysics Laboratory, prior to the 2000 balloon flight mission. In this paper we describe in detail the various steps involved in imaging sources with LXeGRIT and present experimental results on angular resolution and other parameters which characterize its performance as a Compton telescope.