  XTE J1739-302 is a transient X-ray source with unusually short outbursts,
lasting on the order of hours. Here we give a summary of X-ray observations we
have made of this object in outburst with the Rossi X-ray Timing Explorer
(RXTE) and at a low level of activity with the Chandra X-ray Observatory, as
well as observations made by other groups. Visible and infrared spectroscopy of
the mass donor of XTE J1739-302 are presented in a companion paper. The X-ray
spectrum is hard both at low levels and in outburst, but somewhat variable, and
there is strong variability in the absorption column from one outburst to
another. Although no pulsation has been observed, the outburst data from
multiple observatories show a characteristic timescale for variability on the
order of 1500-2000 s. The Chandra localization (right ascension 17h 39m 11.58s,
declination -30o 20' 37.6'', J2000) shows that despite being located less than
2 degrees from the Galactic Center and highly absorbed, XTE J1739-302 is
actually a foreground object with a bright optical counterpart. The combination
of a very short outburst timescale and a supergiant companion is shared with
several other recently-discovered systems, forming a class we designate as
Supergiant Fast X-ray Transients (SFXTs). Three persistently bright X-ray
binaries with similar supergiant companions have also produced extremely short,
bright outbursts: Cyg X-1, Vela X-1, and 1E 1145.1-6141.
