1. Laboratoire National des Champs Magnétiques Pulsés (LNCMP), UMR CNRS-UPS-INSA 5147, Toulouse 31400, France
   
2. H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
   
3. Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews, St Andrews, Fife KY16 9SS, UK

Correspondence to: N. E. Hussey² Correspondence and requests for materials should be addressed to N.E.H. (Email: n.e.hussey@bristol.ac.uk).

The nature of the metallic phase in the high-transition-temperature (high-T _c) copper oxide superconductors, and its evolution with carrier concentration, has been a long-standing mystery¹. A central question is how coherent electronic states, or quasiparticles, emerge from the antiferromagnetic insulator with doping. Recent quantum oscillation experiments on lightly doped copper oxides have shown evidence for small pockets of Fermi surface^{2, 3, 4, 5}, the formation of which has been associated with the opening of the pseudogap—an anisotropic gap in the normal state excitation spectrum of unknown origin¹. As the doping is increased, experiments suggest that the full Fermi surface is restored^{6, 7}, although the doping level at which the pseudogap closes and the nature of the electronic ground state beyond this point have yet to be determined. Here we report the observation of quantum oscillations in the overdoped superconductor Tl₂Ba₂CuO₆₊ that show the existence of a large Fermi surface of well-defined quasiparticles covering two-thirds of the Brillouin zone. These measurements confirm that, in overdoped superconducting copper oxides, coherence is established at all Fermi wavevectors, even near the zone boundary where the pseudogap is maximal and electronic interactions are strongest; they also firmly establish the applicability of a generalized Fermi-liquid picture on the overdoped side of the superconducting phase diagram.