THE clouds of gas in interstellar space also contain grains of dust, whose properties and origins have been the focus of debate for decades. Some dust formation has been assumed to take place in novae explosions(1-5), as was first implied by the observation of a steep decrease in the amount of light emitted by the nova(1,2) DQ Herculis 1934 about 100 days after outburst, presumed to be due to extinction by dust. Here we report observations from the International Ultraviolet Explorer satellite which show directly the onset of dust formation in Nova Cassiopeiae 1993, a classical nova of the same type as DQ Her 1934. The dust formed very quickly-about 70 days after the nova explosion despite the initially high temperature of the ejecta. Our results suggest that high-energy photons are absorbed efficiently by the gas in the ejecta, lowering the temperature in the gas while it is still dense, and thereby allowing molecules to form and then to condense into dust.