A public domain software package is employed in the quasisteady-state simulation of contact angle hysteresis. Three-dimensional sessile drops in equilibrium with a model chemically heterogeneous smooth solid surface are considered; evolving drop shapes, as a function of incremental changes in their volume, are investigated. Results are presented for a model system in which the intrinsic contact angle is assumed to vary along the surface in a periodic manner. Throughout the simulation, calculated contact angles show reasonable agreement with the local intrinsic contact angle values, and the computed drop shapes are found to be constant mean curvature surfaces. Significant hysteresis in the liquid-fluid interface curvature and average contact angle is found; a complete hysteresis loop is simulated. Advancing and receding contact angles exhibit the "stick-slip" behavior observed in experiments as well as in previous 2-D simulations.