  We present observations of molecular gas made with the 15-m James Clark
Maxwell Telescope toward the sites of OH(1720 MHz) masers in three supernova
remnants: W28, W44 and 3C391. Maps made in the 12CO J=3-2 line reveal that the
OH masers are preferentially located along the edges of thin filaments or
clumps of molecular gas. There is a strong correlation between the morphology
of the molecular gas and the relativistic gas traced by synchrotron emission at
centimeter wavelengths. Broad CO line widths (dV=30-50 km/s) are seen along
these gaseous ridges, while narrow lines are seen off the ridges. The ratio of
H2CO line strengths is used to determine temperatures in the broad-line gas of
80 K, and the 13CO J=3-2 column density suggests densities of 10^4-10^5 cm{-3}.
These observations support the hypothesis that the OH(1720 MHz) masers
originate in post-shock gas, heated by the passage of a supernova remnant shock
through dense molecular gas. From the observational constraints on the density,
velocity and magnetic field we examine the physical properties of the shock and
discuss the shock-production of OH. These OH(1720 MHz) masers are useful
``signposts'', which point to the most promising locations to study supernova
remnant/molecular cloud interactions.
