Ab initio calculations have been performed on novel compounds that may greatly expand the scope of rare gas chemistry. These molecules are insertion compounds of xenon into unsaturated hydrocarbons, including acetylene, benzene, and phenol. We present computational evidence that molecules such as H-Xe-C2H, H-Xe-C6H5, and H-Xe-OC6H5 exist. Computational results suggest also the existence of a series of xenon-insertion compounds for larger hydrocarbons of these types. The predictions are not restricted to molecules p with only one xenon atom inserted in them but molecules such as H-Xe-C-2-Xe-H and H-Xe-C-2-XeC2-Xe-H are computationally stable as well. This suggests the existence of linear polymers H-(Xe-C-2)(n)-H for arbitrary large n. All predicted xenon-insertion molecules form a new class of possible precursors and intermediates for synthetic organic and organoelement chemistry.