A very low power Hall effect thruster, known as the narrow channel Hall thruster (NCHT), was recently developed at the Aerospace Plasma Laboratory, Technion. The small dimensions of the NCHT channel (1 mm wide and 2 mm in length) present a challenge for experimental measurements inside it. Instead, in this work, a particle-in-cell (PIC) model of the NCHT discharge is developed capable of providing 2D spatial distributions of the plasma parameters inside the channel. The computed thruster performance is compared to measured global parameters of the thruster, with excellent agreement between simulation results and measurements.