SEVERAL recent experimental findings(1-3) have pointed to a possible route for making an X-ray laser, which could in principle provide an imaging system capable of molecular resolution(4). The method involves the multiphoton excitation of atmos in van der Waals clusters or in molecules to yield ions with core-electron vacancies(1,2),then decay by emission of X-rays, in conjunction with a self-chanelling propagation mode of electromagnetic radiation(3). The multiphoton excitation may be stimulated by ultrahigh-brightness, subpicosecond pulses of laser light(5). We have previously observed(2) emission of X-rays from L-shell transitions in core-excited krypton atmos using this approach. Here we report the multiphoton production of X-rays of wavelength 2-3 Angstrom from highly ionized xenon atmos which possess a large number of inner-shell vacancies while retaining several electrons in relatively weakly bound outer orbitals. Atoms with this ’inverted’ electronic configuration are designated ’hollow atmos’(6,7). We find that generation of hollow atmos can become the dominant excitation mode for such systems, making their exploitation in an X-ray laser a real possibility.