A numerical method has been developed to predict the three-dimensional nonequilibrium flowfield past the space shuttle orbiter at high angles-of-attack (up to 50-deg). An existing viscous shock-layer method for perfect gas flows has been extended to include finite-rate chemical reactions of multi-component ionizing air. A general nonorthogonal computational grid system was introduced to treat the nonaxisymmetric geometry. At shuttle reentry flight conditions, nonequilibrium real gas effects on the surface-measurable quantities are significant. Computational solutions have been obtained for chemically reacting flowfields over the entire windward surface of the space shuttle orbiter at high angles-of-attack. Boundary conditions studied include noncatalytic wall, finite-catalytic wall, fully-catalytic wall, and nonequilibrium slip conditions at the wall and/or shock. The nonequilibrium solutions with a finite-catalytic wall are compared to both fully-catalytic and noncatalytic wall solutions. The present solutions are also compared to chemical equilibrium air solutions, perfect gas solutions, and the shuttle flight heating and pressure data. The comparisons show good agreement and correlations with flight-derived surface heat-transfer and pressure distributions. Three-dimensional effects are clearly shown in the flight-derived data for the first time based upon the results of this study.