A class of extrasolar giant planets--the so-called 'hot Jupiters' (ref. 1)--orbit within 0.05 au of their primary stars (1 au is the Sun-Earth distance). These planets should be hot and so emit detectable infrared radiation. The planet HD 209458b (refs 3, 4) is an ideal candidate for the detection and characterization of this infrared light because it is eclipsed by the star. This planet has an anomalously large radius (1.35 times that of Jupiter), which may be the result of ongoing tidal dissipation, but this explanation requires a non-zero orbital eccentricity (approximately 0.03; refs 6, 7), maintained by interaction with a hypothetical second planet. Here we report detection of infrared (24 microm) radiation from HD 209458b, by observing the decrement in flux during secondary eclipse, when the planet passes behind the star. The planet's 24-microm flux is 55 +/- 10 microJy (1sigma), with a brightness temperature of 1,130 +/- 150 K, confirming the predicted heating by stellar irradiation. The secondary eclipse occurs at the midpoint between transits of the planet in front of the star (to within +/- 7 min, 1sigma), which means that a dynamically significant orbital eccentricity is unlikely.