We present the first ground-based detection of thermal emission from an exoplanet in the H-band. Using HAWK-I on the VLT, we observed an occultation of WASP-19b by its G8V-type host star. WASP-19b is a Jupiter-mass planet with an orbital period of only 19 h, and thus, being highly irradiated, is expected to be hot. We measure an H-band occultation depth of (0.259 +0.046 -0.044) %, which corresponds to an H-band brightness temperature of T_H = 2580 +/- 125 K. A cloud-free model of the planets atmosphere, with no redistribution of energy from day-side to night-side, under predicts the planet/star flux density ratio by a factor of two. As the stellar parameters, and thus the level of planetary irradiation, are well-constrained by measurement, it is likely that our model of the planets atmosphere is too simple.