We explore the properties of atoms confined to the interstitial regions within a carbon nanotube bundle. We find that He and Ne atoms are of ideal size for physisorption interactions, so that their binding energies are much greater there than on planar surfaces of any known material. Hence high density phases exist at even small vapor pressure. There can result extraordinary anisotropic liquids or crystalline phases, depending on the magnitude of the corrugation within the interstitial channels.