Résumé : Context. The remarkable properties of CS 30322-023 became apparent during the course of a high-resolution spectroscopic study of a sample of 23 carbon-enhanced, metal-poor (CEMP) stars. Aims. This sample is studied in order to gain a better understanding of s- and r-process nucleosynthesis at low metallicity, and to investigate the role of duplicity. Methods. High-resolution UVES spectra have been obtained, and abundances are derived using 1-D, plane-parallel OSMARCS models under the LTE hypothesis. The derived atmospheric parameters and observed abundances are compared to evolutionary tracks and nucleosynthesis predictions to infer the evolutionary status of CS 30322-023 Results. CS 30322-023 is remarkable in having the lowest surface gravity (log ≤ -0.3) among the metal-poor stars studied to date. As a result of its rather low temperature (4100 K), abundances could be derived for 35 chemical elements; the abundance pattern of CS 30322-023 is one of the most well-specified of all known extremely metal-poor stars. With [Fe/H] = -3.5, CS 30322-023 is the most metal-poor star to exhibit a clear s-process signature, and the most metal-poor "lead star" known. The available evidence indicates that CS 30322-023 is presently a thermally-pulsing asymptotic giant branch (TP-AGB) star, with no strong indication of binarity thus far (although a signal of period 192 d is clearly present in the radial-velocity data, this is likely due to pulsation of the stellar envelope). Low-mass TP-AGB stars are not expected to be exceedingly rare in a magnitude-limited sample such as the HK survey, because their high luminosities make it possible to sample them over a very large volume. The strong N overabundance and the low 12C/13C ratio (4) in this star is typical of the operation of the CN cycle. Coupled with a Na overabundance and the absence of a strong C overabundance, this pattern seems to imply that hot-bottom burning operated in this star, which should then have a mass of at least 2 M⊙. However, the luminosity associated with this mass would put the star at a distance of about 50 kpc, in the outskirts of the galactic halo, where no recent star formation is expected to have taken place. We explore alternative scenarios in which the observed abundance pattern results from some mixing mechanism yet to be identified occurring in a single low-metallicity 0.8 M⊙ AGB star, or from pollution by matter from an intermediate-mass AGB companion which has undergone hot-bottom burning. We stress, however, that our abundances may be subject to uncertainties due to NLTE or 3D granulation effects which were not taken into consideration. © ESO 2006.