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(Abridged) We present the first results from the Complete Optical and RadioAbsorption Line System (CORALS) survey. We have compiled a homogeneous sampleof radio-selected QSOs from the Parkes Catalogue and searched for damped Lymanalpha systems (DLAs) towards every target, irrespective of its opticalmagnitude. This approach circumvents selection effects -- particularly fromintervening dust -- which have long been suspected to affect DLA surveys inoptically-selected, magnitude-limited QSO samples. The CORALS data set consistsof 66 z_em > 2.2 QSOs in which 22 DLAs with absorption redshifts 1.8 < z_abs <z_em have been identified over a total redshift interval Delta z = 55.46. Inthis first paper of the CORALS series we describe the sample, presentintermediate resolution spectroscopy and determine the population statistics ofDLAs. We deduce a value of the neutral gas mass density traced by DLAs(expressed as a fraction of the closure density) log Omega_DLA h =-2.59^{+0.17}_{-0.24}, and a number density of DLAs per unit redshift n(z) =0.31^{+0.09}_{-0.08}, both at a mean redshift <z> = 2.37. Taking into accountthe errors, we conclude that dust-induced bias in previous surveys may have ledto an underestimate of these quantities by at most a factor of two and we havenot uncovered a previously unrecognised population of high column density DLAsin front of faint QSOs.

The CORALS survey I: New estimates of the number density and gas content of damped Lyman alpha systems free from dust bias