An external cavity has been developed for use with commercial diode lasers. It uses a diffraction grating at grazing incidence for wavelength selection and output coupling. This configuration allows a GaAlAs diode laser to be tuned conveniently anywhere in a range greater than 20 nm. Also, the linewidth is reduced by a factor of more than 1000 from 40 MHz to less than 10 kHz. The new laser system should be useful for high-resolution spectroscopy, laser cooling of atoms, time standards, and coherent optical communications.