We observed three transits of the extrasolar planet HD 189733b in H i Lyman-α and in a few other lines in the ultraviolet with HST/ACS, in the search for atmospheric signatures. We detect a transit signature in the Lyman-α light curve with a transit depth of 5.05 ± 0.75%. This depth exceeds the occultation depth produced by the planetary disk alone at the 3.5σ level (statistical). Other stellar emission lines are less bright, and, taken individually, they do not show the transit signature, while the whole spectra redward of the Lyman-α line has enough photons to show a transit signature consistent with the absorption by the planetary disk alone. The transit depth's upper limits in the emission lines are 11.1% for O i λ1305 Å and 5.5% for C ii λ1335 Å lines. The presence of an extended exosphere of atomic hydrogen around HD 189733b producing 5% absorption of the full unresolved Lyman-α line flux shows that the planet is losing gas. The Lyman-α light curve is well-fitted by a numerical simulation of escaping hydrogen in which the planetary atoms are pushed by the stellar radiation pressure. We constrain the escape rate of atomic hydrogen to be between 10^{9^{and 10^{11^{g s^{-1^{and the ionizing extreme UV flux between 2 and 40 times the solar value (1-σ), with higher escape rates corresponding to larger EUV flux. The best fit is obtained for dM/dt = 10^{10^{g s^{-1^{and an EUV flux F_{EUV_{= 20 times the solar value. HD 189733b is the second extrasolar planet for which atmospheric evaporation has been detected.}}}}}}}}}}}}

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