  3C 397 is a radio and X-ray bright Galactic supernova remnant (SNR) with an
unusual rectangular morphology. Our CO observation obtained with the Purple
Mountain Observatory at Delingha reveals that the remnant is well confined in a
cavity of molecular gas, and embedded at the edge of a molecular cloud (MC) at
the local standard of rest systemic velocity of ~32 km/s. The cloud has a
column density gradient increasing from southeast to northwest, perpendicular
to the Galactic plane, in agreement with the elongation direction of the
remnant. This systemic velocity places the cloud and SNR 3C 397 at a kinematic
distance of ~10.3 kpc. The derived mean molecular density (~10-30 cm^-3)
explains the high volume emission measure of the X-ray emitting gas. A 12CO
line broadening of the ~32 km/s component is detected at the westmost boundary
of the remnant, which provides direct evidence of the SNR-MC interaction and
suggests multi-component gas there with dense (~10^4 cm^-3) molecular clumps.
We confirm the previous detection of a MC at ~38 km/s to the west and south of
the SNR and argue, based on HI self-absorption, that the cloud is located in
the foreground of the remnant. A list of Galactic SNRs presently known and
suggested to be in physical contact with environmental MCs is appended in this
paper.
