We report the detection of molecular clouds around the X-ray bright interior feature in the Galactic supernova remnant (SNR) CTB 109 (G109.1-1.0). This feature, called the Lobe, has been previously suggested to be the result of an interaction of the SNR shock wave with a molecular cloud complex. We present new high resolution X-ray data from the Chandra X-ray Observatory and new high resolution CO data from the Five College Radio Observatory which show the interaction region with the cloud complex in greater detail. The CO data reveal three clouds around the Lobe in the velocity interval -57 < v < -52 km s^-1. The velocity profiles of 12CO at various parts of the east cloud are well fit with a Gaussian; however, at the position where the CO cloud and the Lobe overlap, the velocity profile has an additional component towards higher negative velocities. The molecular hydrogen density in this part of the cloud is relatively high (N_H2 = 1.9 x 10^20 cm^-2), whereas the foreground absorption in X-rays (N_H = 4.5 x 10^21 cm^-2), obtained from Chandra data, is lower than in other parts of the cloud and in the north and south cloud. These results indicate that this cloud has been hit by the SNR blast wave on the western side, forming the bright X-ray Lobe.
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