For the tropical Pacific and Atlantic oceans, internal modes of variability that lead to climatic oscillations have been recognized, but in the Indian Ocean region a similar ocean-atmosphere interaction causing interannual climate variability has not yet been found. Here we report an analysis of observational data over the past 40 years, showing a dipole mode in the Indian Ocean: a pattern of internal variability with anomalously low sea surface temperatures off Sumatra and high sea surface temperatures in the western Indian Ocean, with accompanying wind and precipitation anomalies. The spatio-temporal links between sea surface temperatures and winds reveal a strong coupling through the precipitation field and ocean dynamics. This air-sea interaction process is unique and inherent in the Indian Ocean, and is shown to be independent of the El Niño/Southern Oscillation. The discovery of this dipole mode that accounts for about 12% of the sea surface temperature variability in the Indian Ocean--and, in its active years, also causes severe rainfall in eastern Africa and droughts in Indonesia--brightens the prospects for a long-term forecast of rainfall anomalies in the affected countries.