Understanding the relationship between sea surface temperature (SST) and precipitation is a significant challenge for climate models, particularly for the tropics. Here we present a new monthly coral Sr/Ca record from the tropical Indian Ocean (Chagos Archipelago) that extends from 1950 to 1995. The coral Sr/Ca ratio shows a stationary relationship with local SST, and documents a warming of 0.3 °C since 1950. Previous work has shown that the δ18O values measured in the same coral core provide a proxy record of precipitation in the tropical Indian Ocean. The coral δ18O record shows a nonstationary relationship with local SST, and a correlation between δ18O and SST only emerges in the 1970s. It was proposed that this nonstationary behavior is due to an increase in mean SSTs in the tropical Indian Ocean. During the 1970s, SSTs reached a critical threshold (28.5 °C) beyond which small SST anomalies can have a significant impact on atmospheric convection. As a result, the covariance between SST and precipitation in the tropical Indian Ocean increased. Our new Sr/Ca data confirm that the warming of the Indian Ocean during the late twentieth century affects atmospheric convection and rainfall variability. Moreover, our proxy data show that the relationship between SST and precipitation is nonlinear and characterized by threshold behavior.