Interactions between climate change and non-native invasive species may combine to increase invasion risk to native ecosystems. Changing climate creates risk as new terrain becomes climatically suitable for invasion. However, climate change may also create opportunities for ecosystem restoration on invaded lands that become climatically unsuitable for invasive species. Here, I develop a bioclimatic envelope model for cheatgrass (Bromus tectorum), a non-native invasive grass in the western US, based on its invaded distribution. The bioclimatic envelope model is based on the Mahalanobis distance using the climate variables that best constrain the species' distribution. Of the precipitation and temperature variables measured, the best predictors of cheatgrass are summer, annual, and spring precipitation, followed by winter temperature. I perform a sensitivity analysis on potential cheatgrass distributions using the projections of 10 commonly used atmosphere–ocean general circulation models (AOGCMs) for 2100. The AOGCM projections for precipitation vary considerably, increasing uncertainty in the assessment of invasion risk. Decreased precipitation, particularly in the summer, causes an expansion of suitable land area by up to 45%, elevating invasion risk in parts of Montana, Wyoming, Utah, and Colorado. Conversely, increased precipitation reduces habitat by as much as 70%, decreasing invasion risk. The strong influence of precipitation conditions on this species' distribution suggests that relying on temperature change alone to project future change in plant distributions may be inadequate. A sensitivity analysis provides a framework for identifying key climate variables that may limit invasion, and for assessing invasion risk and restoration opportunities with climate change.