  A spectroscopic technique employing an iodine absorption cell (I_2) to
superimpose a reference spectrum onto a stellar spectrum is currently the most
widely adopted approach to obtain precision radial velocities of solar-type
stars. It has been used to detect ~80 extrasolar planets out of ~130 know. Yet
in its original version, it only allows us to measure precise radial velocities
of single stars. In this paper, we present a novel method employing an I_2
absorption cell that enables us to accurately determine radial velocities of
both components of double-lined binaries. Our preliminary results based on the
data from the Keck I telescope and HIRES spectrograph demonstrate that 20-30
m/s radial velocity precision can be routinely obtained for "early" type
binaries (F3-F8). For later type binaries, the precision reaches ~10 m/s. We
discuss applications of the technique to stellar astronomy and searches for
extrasolar planets in binary systems. In particular, we combine the
interferometric data collected with the Palomar Testbed Interferometer with our
preliminary precision velocities of the spectroscopic double-lined binary HD
4676 to demonstrate that with such a combination one can routinely obtain
masses of the binary components accurate at least at the level of 1.0%.
