IN the binary millisecond pulsar system PSR1957 + 20 (ref. 1), a wind from the pulsar is ablating a low-mass (0.02 solar mass) companion and also inflating a local nebula2 confined by the ram pressure of the interstellar medium. We have detected X-ray emission from this system, using the Rosat satellite. X-ray emission is expected from the pulsar magnetosphere and the two shocks of the pulsar wind, one at the companion and the other inside the nebula. Our observations show that less than 20% of the pulsar's spin-down luminosity can be carried away by electrons and positrons with Lorentz factor gamma almost-equal-to 10(5), and less than 5% by electrons and positrons with gamma almost-equal-to 10(8). Neither of these fluxes can provide the penetrating flux required to heat the companion's photosphere. These observations and those in the accompanying paper by Fruchter et al.3 represent the first direct diagnostics of the relativistic wind from a weakly magnetized pulsar, and suggest that the wind differs substantially from that of the more highly magnetized Crab pulsar.