We have identified a new early T dwarf only 3.6 pc from the Sun, as a common proper motion companion (separation 1459 AU) to the K5V star varepsilon Indi (HD 209100). As such, varepsilon Indi B is one of the highest proper motion sources outside the solar system ( ~ 4.7 arcsec/yr), part of one of the twenty nearest stellar systems, and the nearest brown dwarf to the Sun. Optical photometry obtained from the SuperCOSMOS Sky Survey was combined with approximate infrared photometry from the 2MASS Quicklook survey data release, yielding colours for the source typical of early T dwarfs. Follow-up infrared spectroscopy using the ESO NTT and SOFI confirmed its spectral type to be T2.5 +/- 0.5. With Ks=magnit {11}{2}, varepsilon Indi B is 1.7 mag brighter than any previously known T dwarf and 4 mag brighter than the typical object in its class, making it highly amenable to detailed study. Also, as a companion to a bright nearby star, it has a precisely known distance (3.626+/- 0.009 pc) and relatively well-known age (0.8-2 Gyr), allowing us to estimate its luminosity as log L/ Lsun,=-4.67, its effective temperature as 1260 K, and its mass as ~ 40-60 MJup. varepsilon Indi B represents an important addition to the census of the Solar neighbourhood and, equally importantly, a new benchmark object in our understanding of substellar objects. Based on data from the SuperCOSMOS Sky Surveys and observations collected with the ESO NTT, La Silla, Chile.