GJ 436b is a warm-approximately 800 kelvin-exoplanet that periodically eclipses its low-mass (half the mass of the Sun) host star, and is one of the few Neptune-mass planets that is amenable to detailed characterization. Previous observations(1-3) have indicated that its atmosphere has a ratio of methane to carbon monoxide that is 10(5) times smaller than predicted by models for hydrogen-dominated atmospheres at these temperatures(4,5). A recent study proposed that this unusual chemistry could be explained if the planet's atmosphere is significantly enhanced in elements heavier than hydrogen and helium(6). Here we report observations of GJ 436b's atmosphere obtained during transit. The data indicate that the planet's transmission spectrum is featureless, ruling out cloud-free, hydrogen-dominated atmosphere models with an extremely high significance of 48 sigma. The measured spectrum is consistent with either a layer of high cloud located at a pressure level of approximately one millibar or with a relatively hydrogen-poor (three per cent hydrogen and helium mass fraction) atmospheric composition(7-9).