Strongly polarized X-ray fluorescence from gas-phase molecules has been observed by selectively exciting near core-level ionization thresholds using monochromatized synchrotron radiation. Both the degree and the direction of the polarization are very sensitive to the incident excitation energy, and the symmetry of the occupied and unoccupied molecular orbitals involved in the excitation/fluorescence process. Illustration of the phenomenon will be made using Cl K-edge excitation on the molecule methyl chloride, CH 3Cl. The possibility of extracting orientational, geometrical, and orbital-symmetry information directly from experiment will be discussed, and the importance of the rapid time scale of the X-ray fluorescence decay (≈ 10 fs), which effectively precludes disorientation effects, will be stressed. Expectations are that polarized X-ray emission spectroscopy will enjoy wide applicability to, for example, solids, surfaces and interfaces, oriented molecules such as surface adsorbates, and active sites in macromolecules.