Spectroscopy of the infrared He (I) (10830 angstrom) line with NIRSPEC on Keck and CSHELL at the IRTF, and of the ultraviolet C (III) ( 977) and O (VI) (1032 angstrom) emission with FUSE, reveals that the classical T Tauri star TW Hydrae exhibits P Cygni profiles, line asymmetries, and absorption indicative of a continuous, fast (similar to 400 km s(-1)), hot (similar to 300,000 K) accelerating outflow with a mass-loss rate similar to 10(-11) to 10(-12) M-circle dot yr(-1) or larger. Spectra of T Tau N appear consistent with such a wind. The source of the emission and outflow seems restricted to the stars themselves. Although the mass accretion rate is an order of magnitude less for TW Hya than for T Tau, the outflow reaches higher velocities at chromospheric temperatures in TW Hya. Winds from young stellar objects may be substantially hotter and faster than previously thought.