We describe the structure and implementation of a moving-mesh hydrodynamics solver in the large-scale parallel code, Charm N-body GrAvity solver (ChaNGa). While largely based on the algorithm described by Springel (2010) that is implemented in AREPO, our algorithm differs a few aspects. We describe our use of the Voronoi tessellation library, VORO++, to compute the Voronoi tessellation directly. We also incorporate some recent advances in gradient estimation and reconstruction that gives better accuracy in hydrodynamic solutions at minimal computational cost. We validate this module with a small battery of test problems against the smooth particle hydrodynamics solver included in ChaNGa. Finally, we study one example of a scientific problem involving the mergers of two main sequence stars and highlight the small quantitative differences between smooth particle and moving-mesh hydrodynamics. We close with a discussion of anticipated future improvements and advancements.