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Barnard's star is a red dwarf, and has the largest proper motion (apparent motion across the sky) of all known stars. At a distance of 1.8 parsecs, it is the closest single star to the Sun; only the three stars in the α Centauri system are closer. Barnard's star is also among the least magnetically active red dwarfs known and has an estimated age older than the Solar System. Its properties make it a prime target for planetary searches; various techniques with different sensitivity limits have been used previously, including radial-velocity imaging, astrometry and direct imaging, but all ultimately led to negative or null results. Here we combine numerous measurements from high-precision radial-velocity instruments, revealing the presence of a low-amplitude periodic signal with a period of 233 days. Independent photometric and spectroscopic monitoring, as well as an analysis of instrumental systematic effects, suggest that this signal is best explained as arising from a planetary companion. The candidate planet around Barnard's star is a cold super-Earth, with a minimum mass of 3.2 times that of Earth, orbiting near its snow line (the minimum distance from the star at which volatile compounds could condense). The combination of all radial-velocity datasets spanning 20 years of measurements additionally reveals a long-term modulation that could arise from a stellar magnetic-activity cycle or from a more distant planetary object. Because of its proximity to the Sun, the candidate planet has a maximum angular separation of 220 milliarcseconds from Barnard's star, making it an excellent target for direct imaging and astrometric observations in the future. © 2018, Springer Nature Limited. ; The results are based on observations made with the CARMENES instrument at the 3.5-m telescope of the Centro Astronomico Hispano-Aleman de Calar Alto (CAHA, Almeria, Spain), funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Cientificas (CSIC), the European Union and the CARMENES Consortium members; the 90-cm telescope at the Sierra Nevada Observatory (Granada, Spain) and the 40-cm robotic telescope at the SPACEOBS observatory (San Pedro de Atacama, Chile), both operated by the Instituto de Astrofisica de Andalucia (IAA); and the 80-cm Joan Oro Telescope (TJO) of the Montsec Astronomical Observatory (OAdM), owned by the Generalitat de Catalunya and operated by the Institute of Space Studies of Catalonia (IEEC). This research was supported by the following institutions, grants and fellowships: Spanish MINECO ESP2016-80435-C2-1-R, ESP2016-80435-C2-2-R, AYA2016-79425-C3-1-P, AYA2016-79245-C3-2-P, AYA2016-79425-C3-3-P, AYA2015-69350-C3-2-P, ESP2014-54362-P, AYA2014-56359-P, RYC-2013-14875; Generalitat de Catalunya/CERCA programme; Fondo Europeo de Desarrollo Regional (FEDER); German Science Foundation (DFG) Research Unit FOR2544, project JE 701/3-1; STFC Consolidated Grants ST/P000584/1, ST/P000592/1, ST/M001008/1; NSF AST-0307493; Queen Mary University of London Scholarship; Perren foundation grant; CONICYT-FONDECYT 1161218, 3180405; Swiss National Science Foundation (SNSF); Koshland Foundation and McDonald-Leapman grant; and NASA Hubble Fellowship grant HST-HF2-51399.001. J.T. is a Hubble Fellow.