The atmospheres of a large proportion of white dwarf stars are polluted by heavy elements' that are expected to sink out of visible layers on short timescales(2,3). This has been interpreted as a signature of ongoing accretion of debris from asteroids(4), comets(5) and giant planets(6). This scenario is supported bythe detection of debris discs(7) and transits of planetary fragments(8) around some white dwarfs. However, photospheric metals are only indirect evidence for ongoing accretion, and the inferred accretion rates and parent body compositions heavily depend on models of diffusion and mixing processes within the white dwarf atmosphere(9-11). Here we report a 4.4 sigma detection of X-rays from a polluted white dwarf, G29-38. From the measured X-ray luminosity, we derive an instantaneous accretion rate of M-x =1.63(-0.40)(+1.29) x 10(9) g s(-1), which is independent of stellar atmosphere models. This rate is higher than estimates from past studies of the photospheric abundances of G29-38, suggesting that convective overshoot may be needed to model the spectra of debris-accreting white dwarfs. We measure a low plasma temperature of k(B)T= 0.5 +/- 0.2 keV, corroborating the predicted bombardment solution for white dwarfs accreting at low accretion rates(12)(,13).