In the centres of stars where the temperature is high enough, three alpha-particles (helium nuclei) are able to combine to form 12C because of a resonant reaction leading to a nuclear excited state. (Stars with masses greater than approximately 0.5 times that of the Sun will at some point in their lives have a central temperature high enough for this reaction to proceed.) Although the reaction rate is of critical significance for determining elemental abundances in the Universe, and for determining the size of the iron core of a star just before it goes supernova, it has hitherto been insufficiently determined. Here we report a measurement of the inverse process, where a 12C nucleus decays to three alpha-particles. We find a dominant resonance at an energy of approximately 11 MeV, but do not confirm the presence of a resonance at 9.1 MeV (ref. 3). We show that interference between two resonances has important effects on our measured spectrum. Using these data, we calculate the triple-alpha rate for temperatures from 10(7) K to 10(10) K and find significant deviations from the standard rates. Our rate below approximately 5 x 10(7) K is higher than the previous standard, implying that the critical amounts of carbon that catalysed hydrogen burning in the first stars are produced twice as fast as previously believed. At temperatures above 10(9) K, our rate is much less, which modifies predicted nucleosynthesis in supernovae.