At a distance of 1.295 parsecs, the red-dwarf Proxima Centauri ($α$ Centauri C, GL 551, HIP 70890, or simply Proxima) is the Sun's closest stellar neighbor and one of the best studied low-mass stars. It has an effective temperature of only $\sim$ 3050 K, a luminosity of $\sim$0.1 per cent solar, a measured radius of 0.14 R$_\odot$ and a mass of about 12 per cent the mass of the Sun. Although Proxima is considered a moderately active star, its rotation period is $\sim$ 83 days, and its quiescent activity levels and X-ray luminosity are comparable to the Sun's. New observations reveal the presence of a small planet orbiting Proxima with a minimum mass of 1.3~Earth masses and an orbital period of $\sim$11.2 days. Its orbital semi-major axis is $\sim0.05$ AU, with an equilibrium temperature in the range where water could be liquid on its surface.

Version accepted for publication by Nature (unedited, July 7th, 2016), figures inserted in text for easier read. Article body : 10 pages, 3 figures, 1 table. Methods section : 23 pages, 9 figures, 1 table. IMPORTANT NOTE : Acknowledgment to IAA/CSIC researchers Javier Pascual Granado and Rafael Garrido added for useful discussions and feedback on the mathematical properties of time-series