ANTARES is a high-energy neutrino telescope installed in the Mediterranean Sea at a depth of 2475 m. It consists of a three-dimensional array of optical modules, each containing a large photomultiplier tube. A total of 2700 front-end ASICs named analogue ring samplers (ARS) process the phototube signals, measure their arrival time, amplitude and shape as well as perform monitoring and calibration tasks. The ARS chip processes the analogue signals from the optical modules and converts information into digital data. All the information is transmitted to shore through further multiplexing electronics and an optical link. This paper describes the performance of the ARS chip: results from the functionality and characterization tests in the laboratory are summarized and the long-term performance in the apparatus is illustrated. ; 20 páginas, 22 figuras, 2 tablas.-- et al.(ANTARES Collaboration). ; The authors acknowledge the financial support of the funding agencies: Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commission Européenne (FEDER fund and Marie Curie Program), Région Alsace (contrat CPER), Région Provence-Alpes-Côte d'Azur, Département du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium für Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Stichting voor Fundamenteel Onderzoek der Materie (FOM), Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of the Russian Federation for young scientists and leading scientific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania; Ministerio de Ciencia e Innovación (MICINN), Prometeo of Generalitat Valenciana (GVA) and MultiDark, Spain. We also acknowledge the technical support of Ifremer, AIM and Foselev Marine for the sea operation and the CC-IN2P3 for the computing facilities and the financial support of the French Agence National de la Recherche under the contract number ANR-08-JCJC-0061-01.