Recent statistical studies suggest yields for major U.S. food crops will dramatically decrease under climate change due to the rise of extreme temperatures over the growing season. However, these results do not account for changes in the crop mix, therefore overestimating potential damages to the sector. In this study we seek to determine how the crop mix and growing regions would shift in response to climate change. The paper develops a dynamic multinomial discrete choice framework to model adaptation to climate change through crop choice. A major innovation of this study is the construction of a very large high-resolution data set for the econometric analysis and the computational procedure developed to obtain estimates. We combine data on crop cover (USDA Cropland Data Layer (CDL), 30*30 meter resolution) and climate variables (PRISM, 4*4 km resolution) for the study region, matched with crop prices and production costs at regional level. The data set provides billions of spatial units from which we sample for the spatial analysis. The main advantage of such an extensive and detailed data set is the careful consideration of the spatial heterogeneity within counties. The generality of our empirical framework allows prediction of crop choices at field level under various climate change scenarios. The preliminary empirical results show that both market state variables (yields, prices, and costs) and crop state variables (related to crop rotations) are important predictors of farmers' crop choice at field level.