A maximum a posteriori (MAP) estimation method is described for enhancing the spatial resolution of a hyperspectral image using a higher resolution coincident panchromatic image. The approach makes use of a stochastic mixing model (SMM) of the underlying spectral scene content to develop a cost function that simultaneously optimizes the estimated hyperspectral scene relative to the observed hyperspectral and panchromatic imagery, as well as the local statistics of the spectral mixing model. The incorporation of the stochastic mixing model is found to be the key ingredient for reconstructing subpixel spectral information in that it provides the necessary constraints that lead to a well-conditioned linear system of equations for the high-resolution hyperspectral image estimate. Here, the mathematical formulation of the proposed MAP method is described. Also, enhancement results using various hyperspectral image datasets are provided. In general, it is found that the MAP/SMM method is able to reconstruct subpixel information in several principal components of the high-resolution hyperspectral image estimate, while the enhancement for conventional methods, like those based on least squares estimation, is limited primarily to the first principal component (i.e., the intensity component).