Conservation scientists emphasize the importance of maintaining a connected network of protected areas to prevent ecosystems and populations from becoming isolated, reduce the risk of extinction, and ultimately sustain biodiversity. Keeping protected areas connected in a network is increasingly recognized as a conservation priority in the current era of rapid climate change. Models that identify suitable linkages between core areas have been used to prioritize potentially important corridors for maintaining functional connectivity. Here, we identify the most "natural" (i.e., least human-modified) corridors between large protected areas in the contiguous Unites States. We aggregated results from multiple connectivity models to develop a composite map of corridors reflecting agreement of models run under different assumptions about how human modification of land may influence connectivity. To identify which land units are most important for sustaining structural connectivity, we used the composite map of corridors to evaluate connectivity priorities in two ways: (1) among land units outside of our pool of large core protected areas and (2) among units administratively protected as Inventoried Roadless (IRAs) or Wilderness Study Areas (WSAs). Corridor values varied substantially among classes of "unprotected" non-core land units, and land units of high connectivity value and priority represent diverse ownerships and existing levels of protections. We provide a ranking of IRAs and WSAs that should be prioritized for additional protection to maintain minimal human modification. Our results provide a coarse-scale assessment of connectivity priorities for maintaining a connected network of protected areas.