We present radio observations of the bright compact SNR 3C 391 (G31.9+0.0) made with the VLA2 at 6 arcsec resolution. The remnant's morphology suggests expansion into a medium with a very strong density gradient. We interpret radio and X-ray morphologies as evidence for a breakout of the expanding material into a region of abruptly lower density. The CO survey of Sanders et al. (1986), though not fully sampled, shows the presence of molecular gas at the position of the remnant, with a radial velocity of 90-110 km/s similar to the highest velocity absorption features seen in H I toward 3C 391. This gas may thus be near the remnant, though direct evidence of interaction is lacking. More detailed CO observations, and searches for evidence of shocked molecular gas such as 2.12 micron emission from H2, might confirm or refute the tantalizing possibility that 3C 391 is interacting with an observable molecular cloud.