High-resolution (9" x 6") CO (J = 1 --> 0) observations in the barred spiral galaxy M83 reveal a massive molecular gas complex associated with luminous H II regions at the southern bar-spiral arm transition zone. The cloud complex is resolved into two principal components, one of which is clearly linked to the bar, the other to the spiral arm. The bar component is located along a ridge of highly polarized radio continuum emission at the place where the ridge bends away from following the bar to following the spiral arm. The spiral arm component is located at the same galaxy azimuth as the bar component, but 250 pc further out in radius, just upstream from a ridge of H II regions on the spiral arm. Gas dynamical mechanisms are identified which impart a shear in this region, giving the spiral arm component a tangential velocity 60 km s-1 (in the plane of the disk) greater than the bar component. Numerous bright H II regions are associated with the spiral arm gas, but very few are associated with the bar gas, suggesting that massive stars form more efficiently in the spiral arms than on the bar. The CO morphology and kinematics are consistent with the entire molecular complex originating through orbit crowding, in which gas on highly elliptical orbits from the bar region converges with gas on more circular orbits from the region just beyond the bar. The orbit crowding is strongly enhanced by radial streaming motions due to density waves, which are in opposite directions along the bar and spiral arm, thereby producing a region of streamline convergence where the bar meets the spiral arm. The regions of enhanced massive star formation near the bar ends of many barred galaxies are probably due to orbit crowding effects like those observed in M83.