Aim To investigate the relationship between chiropteran species distributions and four fundamental environmental factors — temperature, precipitation, soil and vegetation — and to construct a species richness prediction map based on the environmental factors. Location The state of Michoacán, México. Methods Bat specimens collected during a 2‐year project were combined with museum specimens to form a dataset of over 3200 entries pertaining to 71 species of bats. Coordinates of the collection localities were recorded with GPS receivers or determined from maps. ArcView GIS was used to characterize the distribution of the species relative to the four environmental factors by projecting coordinates of the collection sites onto digitized maps of those factors. Correspondence analysis (CA) was used to evaluate the relationship between species distributions and the environmental factors. Results The CA results indicated that the order of importance of these factors is (from highest to lowest): temperature, vegetation, precipitation and soil. A predicted distribution map was constructed for each species of bat, based on the result of the CA analysis, using correspondences of each species to climate, vegetation and precipitation. Soil types were excluded from the prediction model because soil type does not appear to carry high predictive value for bat species in Michoacán. Distribution maps of the 71 bat species were then overlaid to generate a map of bat species richness for the state of Michoacán. Main conclusions  Neither family membership nor feeding guild affiliation appear to play important roles in chiropteran species distributions in Michoacán. The bat species richness prediction map will be a useful tool for conservation works in the region.