Muonium adds to the unsaturated bond in 1,3-dithiolane-2-thione or -2-selenone to form a chalcogen-centered radical. The muon hyperfine coupling constants (hfc) were measured for both compounds over a range of temperatures. In solution, the temperature dependence of the muon hfc indicates that for the thiyl radical the preferred conformation corresponds to the muon eclipsing the unpaired electronp z-orbital, while there is practically free rotation in the case of the selenenyl radical in the temperature range studied. In pure thione the hfc values show a remarkable discontinuity at the melting point. The two radical signals seen in the solid are interpreted as due to the presence of two dominant crystal orientations in the samples studied. In pure selenone data were obtained only in the solid. For both systems, the solid phase results show that interaction between the muon and the unpaired electron spin is enhanced compared to the liquid phase and/or the solution.