A new technique sensitive to molecular orientation and geometry, and based on measuring the polarization of x-ray emission, has been applied to the Cl-containing molecules methyl chloride (CH3Cl) and the chlorofluoromethanes (CF3Cl, CF2Cl2, and CFCl3) in the gas phase. Upon selective excitation using monochromatic synchrotron radiation in the Cl K-edge (Cl ls) near-threshold region, polarization-selective x-ray emission studies reveal highly polarized molecular valence x-ray fluorescence for all four molecules. The degree and the orientation of the polarized emission are observed to be sensitive to the incident excitation energy near the Cl K edge. In some cases, the polarization direction for x-ray emission reverses for small changes in incident excitation energy (a few eV). It is shown that the polarized x-ray emission technique can be used to infer, directly from experiment, symmetries of occupied and unoccupied valence molecular orbitals, anisotropies in absorption and emission, and orientational and geometrical information. It is suggested that the x-ray polarized-fluorescence phenomenon, reported here for simple molecules, can be used as a new approach to study more complicated systems in a variety of environments.