RX J1713.7–3946 is one of the TeV γ-ray supernova remnants (SNRs) emitting synchrotron X-rays. The SNR is associated with molecular gas located at ~1 kpc. We made new molecular observations toward the dense cloud cores, peaks A, C, and D, in the SNR in the 12CO(J = 2-1) and 13CO(J = 2-1) transitions at an angular resolution of 90''. The most intense core in 13CO, peak C, was also mapped in the 12CO(J = 4-3) transition at an angular resolution of 38''. Peak C shows strong signs of active star formation including bipolar outflow and a far-infrared protostellar source, and has a steep gradient with a r –2.2±0.4 variation in the average density within radius r. Peak C and the other dense cloud cores are rim-brightened in synchrotron X-rays, suggesting that the dense cloud cores are embedded within or on the outer boundary of the SNR shell. This confirms the earlier suggestion that the X-rays are physically associated with the molecular gas. We present a scenario where the densest molecular core, peak C, survived the blast wave and is now embedded within the SNR. Numerical simulations of the shock-cloud interaction indicate that a dense clump can indeed survive shock erosion, since the shock propagation speed is stalled in the dense clump. Additionally, the shock-cloud interaction induces turbulence and magnetic field amplification around the dense clump that may facilitate particle acceleration in the lower-density inter-clump space leading to enhanced synchrotron X-rays around dense cores.