Tree cover varies enormously across tropical ecosystems-from arid savannas to closed rain forests-and yet a general predictive theory of tropical tree cover remains elusive. Here we use the maximum-entropy method to predict the most likely sample frequency distribution of ecosystems with different tree and grass fractional cover if balance between water supply and demand were the dominant constraint on community assembly. Assuming a hierarchy of individual plant water demand in which trees require more water than grasses, we reproduce observed trends in the means and the upper and lower limits of tropical tree and grass cover across the entire spectrum of tropical ecosystem water supply. Finer details not captured by our predictions indicate the influence of additional factors, such as disturbance. Our results challenge the view that tropical tree-grass coexistence is largely sustained by disturbances in moist environments ("unstable" coexistence) with water supply playing a dominant role only in arid conditions ("stable" coexistence). More generally, they suggest that macroecological patterns can be understood and predicted as the most likely outcome of a large number of stochastic processes being played out within a relatively small number of ecological constraints.