To allow the use of detailed chemical modules in three-dimensional global forecast and climate models, it is necessary to have efficient and accurate solvers for the chemical species that allow for diurnal forcing. The aim of this work was to develop a fast chemistry solver based on the implicit Euler finite difference approximation to the chemical continuity equation for a set of chemical species. This finite difference form of the continuity equation is appealing because of its mass-conserving properties. We employ two algorithms for solution: a basic Newton solver and a modification of this method, which we have dubbed the reduced Jacobian (RJ) solver. Both methods yield equivalent solutions, but the RJ solver can be 10 times more efficient on a scalar machine for fixed time stepping. Both methods are evaluated for accuracy and timing against the Gear solver. The RJ algorithm breaks the Jacobian matrix into smaller units that may be solved more efficiently. To do this, we have made use of the interactiveness of family species. The reduction in computational time makes this method a good candidate for three-dimensional modeling of atmospheric chemistry. In this paper we discuss the method and present a chemical box model comparison of these three techniques for a chemical set comprising Ox, HOx, NOx, ClOx, BrOx, and CH4 oxidation gas-phase chemistry, at various heights in the atmosphere ranging from the upper troposphere to the mesosphere. We have also tested a modification that reduces errors at sunrise and sunset without seriously compromising the efficiency of the method. From our tests it would appear that the RJ solver is robust at all heights tested and should be readily adapted to other chemical mechanisms.¿ 1997 American Geophysical Union