Infrared radiation emitted from a planet contains information about the chemical composition and vertical temperature profile of its atmosphere(1-3). If upper layers are cooler than lower layers, molecular gases will produce absorption features in the planetary thermal spectrum(4,5). Conversely, if there is a stratosphere-where temperature increases with altitude-these molecular features will be observed in emission(6-8). It has been suggested that stratospheres could form in highly irradiated exoplanets(9,10), but the extent to which this occurs is unresolved both theoretically(11,12) and observationally(3,13-15). A previous claim for the presence of a stratosphere(14) remains open to question, owing to the challenges posed by the highly variable host star and the low spectral resolution of the measurements(3). Here we report a near-infrared thermal spectrum for the ultrahot gas giant WASP-121b, which has an equilibrium temperature of approximately 2,500 kelvin. Water is resolved in emission, providing a detection of an exoplanet stratosphere at 5 sigma confidence. These observations imply that a substantial fraction of incident stellar radiation is retained at high altitudes in the atmosphere, possibly by absorbing chemical species such as gaseous vanadium oxide and titanium oxide.