The presence of clouds on hot giant exoplanets has been known for several years, but the usual method of their identification — transmission spectroscopy — is only sensitive to high-altitude clouds located near the planetary terminator. This has restricted our ability to measure cloud properties deeper within the atmosphere and provided little information about the longitudinal extent of clouds. Our understanding of the global cloud properties on these planets is therefore limited, and hence clouds often cannot be included in one-dimensional and three-dimensional atmosphere simulations. We report on new observations of the thermal phase curve of the highly irradiated brown dwarf KELT-1b taken with HST/WFC3. KELT-1b’s high surface gravity means that, unlike on an average hot Jupiter, water should still be present in significant quantities on the planetary dayside, and our observations show strong spectral variation in the 1.4um water feature — indicative of variable cloud cover. These observations allow us, for the first time, to measure the cloud coverage as a function of longitude, and thereby create a detailed cloud map of KELT-1b.