A new type of survey for galaxies with z > 2 will be described. The idea is to search for the spectroscopic imprint that the H1 disc of a foreground galaxy leaves on radiation emitted by a background Qso; namely, a Lyman-α absorption line broadened by radiation damping. A continuing survey has revealed the presence of 15 damped Lα lines with redshifts between 1.8 and 2.8 in the spectra of 68 QSOS. In comparison, no more than three discs with the properties of nearby galaxies should have been detected. Furthermore, the mean column density of the 15 absorbers, <(N(H1)> = 1.4 x 10
21
cm
-2
, is much larger than expected for the outskirts of H1 discs. Both statistical and physical evidence has accumulated which suggests that the damped Lα systems are a distinct population of absorbers with properties reminiscent of H1 discs. First, the Lyman-α absorption lines detected in the survey follow a frequency distribution of equivalent width that cannot be due to previously detected cloud populations. At large equivalent widths, where the damped Lα lines occur, a new population of absorbers must exist. This damped population is therefore unrelated to clouds that are known to differ physically from galaxy discs. Secondly, detailed studies of the damped population reveal many of the properties shared by the H1 discs of galaxies. For example, (
a
) the absorption spectra due to ions of abundant elements are dominated by low ions such as C
+
, Si
+
and Fe
+
, instead of C3
+
and Si
3+
, which are usually seen and (
b
) the recent detection of 21 cm absorption at z = 2.04 in one of the damped systems shows that the H1 is cold and that it has a low level of turbulence (σ ≈ 10 km s
-1
). Another piece of evidence connecting the damped population with discs is that the cosmological mass density of the absorbers is characterized by a density parameter, Ω≈ 3 x 10
-3
/
h
. This is comparable to the Ω due to luminous baryons. We suggest that this agreement is not coincidental, but rather reflects the fact that we have detected the progenitors of the baryon content of nearby galaxies. The discovery of the damped population has a number of implications for theories of galaxy formation. First, if the damped absorbers are identified with the normal population of galaxies, the H1 discs at z > 2 have radii ≈ 3 R
HO
(Holmberg). Because their redshift distribution is consistent with formation at z > 2.8, the production of large H1 discs from the collapse of protogalaxies must occur more rapidly (within less than 3 Ga) than predicted in many theories. Secondly, the collapse to discs of present size must occur in the galactic plane rather than from the halo.