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30 Doradus C is a superbubble that emits the brightest non-thermal X- and TeV gamma-rays in the Local Group. To explore the detailed connection between the high-energy radiation and the interstellar medium, we have carried out new CO and H i observations using the Atacama Large Millimeter/Submillimeter Array (ALMA), Atacama Submillimeter Telescope Experiment, and the Australia Telescope Compact Array with resolutions of up to 3 pc. The ALMA data of 12CO(J = 1–0) emission revealed 23 molecular clouds, with typical diameters of ∼6–12 pc and masses of ∼600–10,000 M⊙. A comparison with the X-rays of XMM–Newton at ∼3 pc resolution shows that X-rays are enhanced toward these clouds. The CO data were combined with the H i to estimate the total interstellar protons. A comparison of the interstellar proton column density and the X-rays revealed that the X-rays are enhanced with the total proton column density. These are most likely to be caused by the shock-cloud interaction, which is modeled by magnetohydrodynamical simulations (Inoue et al. 2012). We also note a trend for the X-ray photon index to vary with distance from the center of the high-mass star cluster. This suggests that the cosmic-ray electrons are accelerated by one or multiple supernovae in the cluster. Based on these results, we discuss the role of the interstellar medium in cosmic-ray particle acceleration. [ABSTRACT FROM AUTHOR]