Of the over 200 known extrasolar planets, 14 exhibit transits in front of their parent stars as seen from Earth. Spectroscopic observations of the transiting planets can probe the physical conditions of their atmospheres. One such technique can be used to derive the planetary spectrum by subtracting the stellar spectrum measured during eclipse (planet hidden behind star) from the combined-light spectrum measured outside eclipse (star + planet). Although several attempts have been made from Earth-based observatories, no spectrum has yet been measured for any of the established extrasolar planets. Here we report a measurement of the infrared spectrum (7.5-13.2 microm) of the transiting extrasolar planet HD 209458b. Our observations reveal a hot thermal continuum for the planetary spectrum, with an approximately constant ratio to the stellar flux over this wavelength range. Superposed on this continuum is a broad emission peak centred near 9.65 microm that we attribute to emission by silicate clouds. We also find a narrow, unidentified emission feature at 7.78 microm. Models of these 'hot Jupiter' planets predict a flux peak near 10 microm, where thermal emission from the deep atmosphere emerges relatively unimpeded by water absorption, but models dominated by water fit the observed spectrum poorly.