In solution, spin-polarization transfer between laser-polarized xenon and the hydrogen nuclei of nearby molecules leads to signal enhancements in the resolved H-1 NMR spectrum, offering new opportunities for probing the chemical environment of xenon atoms. Following binding of laser-polarized xenon to molecules of cryptophane-A, selective enhancements of the H-1 NMR signals were observed. A theoretical framework for the interpretation of such experimental results is provided, and the spin polarization-induced nuclear Overhauser effects are shown to yield information about the molecular environment of xenon. The observed selective H-1 enhancements allowed xenon-proton internuclear distances to be estimated. These distances reveal structural characteristics of the complex, including the preferred molecular conformations adopted by cryptophane-A upon binding of xenon.