THE Lyman-alpha absorption lines observed in the spectra of quasars are thought to be caused by intervening clouds of atomic hydrogen, the origin and physical nature of which are still unknown. These clouds might be structures confined by the pressure of the surrounding intergalactic medium(1), relicts of density fluctuations in the early Universe(2), gravitationally bound clouds associated with condensations of cold dark matter(3) or the result of shocks owing to galaxy formation(4). Here we present ultraviolet spectra of the quasar pair Q0107 - 025A and B, in which we detect four Lyman-alpha lines common to both spectra in the redshift range 0.5 < z < 0.9. These common lines indicate that the characteristic radius of the clouds has a lower limit of 160h(-1) kpc, where h is the Hubble constant in units of 100 km s(-1) Mpc(-1). The typical velocity difference between the common absorption lines along the two lines of sight is only about 100 km s(-1). The clouds are larger in extent and have smaller internal motions than can be explained by any current model.