X-ray emission from supernova 1987A has been observed continually by the Ginga satellite since July 1987. The observed X-ray spectrum1,2 has two components: hard X-rays, above 15 keV in energy, have a nearly flat spectrum, and are thought to be Compton-degraded γ-rays from the decay of 56Co (ref. 3); the soft component (<15 keV) shows a thermal bremsstrahlung spectrum with a temperature of 10 to 12 keV, and may be due to thermal emission from shock-heated ejecta4. In January 1988, X-ray emission in the range 6–16 keV flared up, on a timescale of a few weeks, to about three times the level of the previous three months5. Here we interpret the flaring as the result of interaction of the supernova ejecta with pre-existing circumstellar matter, whose density distribution was peaked because material blown off from the progenitor star ran into slower-moving material ejected during an earlier stage of the star's life.