It is possible to generate very bright sub-picosecond pulses of spontaneous x-ray radiation utilizing the electron beam from the SLAC linear accelerator and an undulator. The present injection-damping ring system used to inject into the PEP-II B-Factory can be used for this purpose, without any modification to the linear accelerator expect for a sequence of 4 bending magnets to compress the electron bunch. With a charge of 3.4 nC per bunch accelerated to 28 GeV and a 10 m long undulator, it is quite feasible to generate pulses of x-rays of 8.3 kV energy (in a spectrum extending to over 1 MeV), 80 fsec long (full-width-half-maximum), with a peak brightness of the order of 1025 photons/(secXmm2Xmrad2X0.1% bandwidth), and 108 photons per pulse in a 0.1% bandwidth.