  We demonstrate a straight-forward technique to measure the linewidth of a
grating-stabilized diode laser system---known as an external cavity diode laser
(ECDL)---by beating the output of two independent ECDLs in a Michelson
interferometer, and then taking the Fourier transform of the beat signal. The
measured linewidth is the sum of the linewidths of the two laser systems.
Assuming that the two are equal, we find that the linewidth of each ECDL
measured over a time period of 2 \textmu s is about 0.3 MHz. This narrow
linewidth shows the advantage of using such systems for high-resolution
spectroscopy and other experiments in atomic physics.
