A second-order numerical method of characteristics was used to solve the equations of motion for three-dimensional, steady, supersonic, nonequilibrium, chemically reacting flow of a system of thermally perfect gases in an exhaust nozzle. A production type computer program which is capable of solving a wide variety of supersonic nozzle problems was developed for the CDC-6500 computer. A bicharacteristic method of characteristics due to D.S. Butler and a special implicit method for the species continuity equations were employed. The chemical kinetic model considers 19 species formed from the 6 elements--carbon, hydrogen, ocygen, nitrogen, flourine and chlorine--and 48 chemical reactions (13 dissociation-recombination reactions and 35 binary exchange reactions). In addition to the nonequilibrium chemistry model, the program also considers frozen and equilibrium flows, and flows with constant specific heat ratios. The absolute accuracy and order of accuracy of the method was shown by comparing the computed solution for spherical source flow with the exact solution for isentropic flow, and by comparing the computed solution for an axisymmetric, nonequilibrium flow with the results of an existing two-dimensional method. (Author).