The eruptive activity of a volcano is fundamentally controlled by the rate of magma supply. At Kilauea Volcano, Hawai'i, the rate of magma rising from a source within Earth's mantle, through the Hawaiian hotspot, was thought to have been relatively steady in recent decades. Here we show that the magma supply to Kilauea at least doubled during 2003-2007, resulting in dramatic changes in eruptive activity and the formation of new eruptive vents. An initial indication of the surge in supply was an increase in CO2 emissions during 2003-2004, combined with the onset of inflation of Kilauea's summit, measured using the Global Positioning System and interferometric synthetic aperture radar. Inflation was not limited to the summit magma reservoirs, but was recorded as far as 50 km from the summit, implying the existence of a connected magma system over that distance. We also record increases in SO2 emissions, heightened seismicity, and compositional and temperature variations in erupted lavas. The increase in the volume of magma passing through and stored within Kilauea, coupled with increased CO2 emissions, indicate a mantle source for the magma surge. We suggest that magma supply from the Hawaiian hotspot can vary over timescales of years, and that CO2 emissions could be a valuable aid for assessing variations in magma supply at Kilauea and other volcanoes.