We report the discovery of five T Tauri star systems, two of which are resolved binaries, in the vicinity of the nearest known region of recent star formation, the TW Hydrae Association. The newly discovered systems display the same signatures of youth (namely high X-ray flux, large Li abundance and strong chromospheric activity) and the same proper motion as the original five members. These similarities firmly establish the group as a bona fide T Tauri association, unique in its proximity to Earth and its complete isolation from any known molecular clouds. At an age of ~10 Myr and a distance of ~50 pc, the association members are excellent candidates for future studies of circumstellar disk dissipation and the formation of brown dwarfs and planets. Indeed, as an example, our speckle imaging revealed a faint, very likely companion 2 north of CoD-33 7795 (TWA 5). Its color and brightness suggest a spectral type ~M8.5 which, at an age of ~10^7 years, implies a mass ~20 M(Jupiter).