We have investigated the molecular environment of the semicircular composite supernova remnant ( SNR ) 3C 396 and performed a Chandra spatially resolved thermal X-ray spectroscopic study of this young SNR . With our CO millimeter observations , we find that the molecular clouds ( MCs ) at V _ { LSR } \sim 84 km s ^ { -1 } can better explain the multiwavelength properties of the remnant than the V _ { LSR } = 67–72 km s ^ { -1 } MCs that are suggested by Lee et al . ( 2009 ) . At around 84 { km } { s } ^ { -1 } , the western boundary of the SNR is perfectly confined by the western molecular wall . The CO emission fades out from west to east , indicating that the eastern region is of low gas density . In particular , an intruding finger/pillar-like MC , which may be shocked at the tip , can well explain the X-ray and radio enhancement in the southwest and some infrared filaments there . The SNR–MC interaction is also favored by the relatively elevated ^ { 12 } CO J =2–1/ J =1–0 line ratios in the southwestern “ pillar tip ” and the molecular patch on the northwestern boundary . The redshifted ^ { 12 } CO ( J =1–0 and J =2–1 ) wings ( 86–90 km s ^ { -1 } ) of an eastern 81 { km } { s } ^ { -1 } molecular patch may be the kinematic evidence for shock–MC interaction . We suggest that the 69 km s ^ { -1 } MCs are in the foreground based on HI self-absorption while the 84 km s ^ { -1 } MCs at a distance of 6.2 kpc ( the tangent point ) are in physical contact with SNR 3C 396 . The X-ray spectral analysis suggests an SNR age of \sim 3 kyr . The metal enrichment of the X-ray emitting gas in the north and south implies a 13– 15 M _ { \odot } B1–B2 progenitor star .