TRACE has been selected as a NASA Small Explorer mission for development and flight in late 1997. The TRACE science investigation explores the connections between fine-scale magnetic fields and the associated plasma structures on the Sun. The instrument collects images of solar plasmas at temperatures from 104 to 107 degrees K, with one arc second spatial resolution (5 times better than SXT on Yohkoh) and excellent temporal resolution and continuity. By observing together in 1997-8, TRACE and SoHO will gather simultaneous, digital measurements of all the temperature regimes of the solar atmosphere, in both high-resolution imaging and spectroscopy, and magnetograms of the photosphere. The 30 cm aperture TRACE telescope uses three normal-incidence coatings for the EUV and one for the UV on quadrants of the primary and secondary mirrors. Interference filters further isolate 5 different UV bands. The images are coaligned and internally stabilized against spacecraft jitter. A 1024 x 1024 CCD detector collects images over an 8.5 x 8.5 arc minute field of view. TRACE will be launched on a GSFC SMEX spacecraft into a Sun-synchronous orbit, allowing continuous observing for 8 months of the baseline 1-year mission. It will be operated in coordination with the SoHO Experiment Operations Facility at GSFC. LPARL, SAO, and GSFC will develop the instrument, directed by PI Alan Title. Designs, flight spare components, and software from the MDI, SXT, SPDE, and NIXT programs will be used. TRACE will be an open mission: the PI and co-I's have waived all priority data rights, and all data and analysis software will be freely available to the space science community.