We demonstrate correlated rapid variability between the optical/UV and
X-ray emission for the first time in a soft X-ray transient, GRO J165
5-40: Hubble Space Telescope (HST) light curves show similar features
to those seen by the Rossi X-my Timing Explorer (RXTE), but with mean
delay of up to 10-20 s. We interpret the correlations as the result of
reprocessing of X-rays into optical and UV emission, with a delay owi
ng to finite light travel time, and thus perform echo mapping of the s
ystem. The time-delay distribution has a mean of 14.6 +/- 1.4 s and di
spersion (i.e. the standard deviation of the distribution) of 10.5 +/-
1.9 s at binary phase 0.4. Hence we identify the reprocessing region
as the accretion disc rather than the mass donor star.