We report on the Design Study of a Free-Electron-Laser experiment designed to produce coherent radiation at the wavelength of 1.5 Angstrom and longer. The proposed experiment utilizes 1/3 of the SLAC linac to accelerate electrons to 15 GeV. The high brightness:electron beam interacts with the magnetic field of a long undulator and generates coherent radiation by self-amplified spontaneous emission (SASE). The projected output peak power is about 10 GW. The project presents several challenges in the realization of a high brightness electron beam, in the construction and tolerances of the undulator and in the transport of the x-ray radiation. The technical solutions adapted far the design are discussed. Numerical simulations are used to show the performance as a function of system parameters.