The Linac Coherent Light Source has added a self-seeding capability to the soft x-ray range using a grating monochromator system. We report the demonstration of soft x-ray self-seeding with a measured resolving power of 2000-5000, wavelength stability of 10(-4), and an increase in peak brightness by a factor of 2-5 across the photon energy range of 500-1000 eV. By avoiding the need for a monochromator at the experimental station, the self-seeded beam can deliver as much as 50-fold higher brightness to users.