A new algorithm for fitting atomic charges to molecular electrostatic potentials is presented. This method is non-iterative and rapid compared to previous work. Results from a variety of gaussian basis sets, including STO-3G, 3-21G and 6-31G*, are presented. Charges for a representative collection of molecules, comprising both first and second row atoms and anions are tabulated. The effects of using experimental and optimized geometries are explored. Charges derived from these fits are found to adequately reproduce SCF dipole moments. A small split valence representation, 3-21G, appears to yield consistently good results in a reasonable amount of time.