In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum(1,2). The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now know governs the world at the atomic scale. Since then, studies involving the Lyman-alpha line-the 1S-2P transition at a wavelength of 121.6 nanometres-have played an important part in physics and astronomy, as one of the most fundamental atomic transitions in the Universe. For example, this transition has long been used by astronomers studying the intergalactic medium and testing cosmological models via the so-called 'Lyman-alpha forest('3) of absorption lines at different redshifts. Here we report the observation of the Lyman-alpha transition in the antihydrogen atom, the antimatter counterpart of hydrogen. Using narrow-line-width, nanosecond-pulsed laser radiation, the 1S-2P transition was excited in magnetically trapped antihydrogen. The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 +/- 0.12 gigahertz (1 sigma uncertainty) and agrees with the prediction for hydrogen to a precision of 5 x 10(-8). Comparisons of the properties of antihydrogen with those of its well-studied matter equivalent allow precision tests of fundamental symmetries between matter ;and antimatter. Alongside the ground-state hyperfine(4,5) and 1S-2S transitions(6,7) recently observed in antihydrogen, the Lyman-alpha transition will permit laser cooling of antihydrogen(8,9), thus providing a cold and dense sample of anti-atoms for precision spectroscopy and gravity measurements(10). In addition to the observation of this fundamental transition, this work represents both a decisive technological step towards laser cooling of antihydrogen, and the extension of antimatter spectroscopy to quantum states possessing orbital angular momentum.