The structure and stability of VF5 and the higher chromium fluorides CrF4, CrF5, and CrF6 have been investigated using density functional theory. The local density approximation (LDA) was used to obtain geometries and vibrational frequencies, while nonlocal corrections were added in order to obtain more accurate binding energies. The results obtained for CrF4 and VF5 are in good agreement with the available experimental data, indicating the quality of the method used. Both CrF5 and CrF6 are found to be stable with respect to Cr-F dissociation. The calculated binding energies are 49.7 and 40.7 kcal/mol, respectively. In agreement with recent ab initio work, the octahedral isomer is found to be the most stable for CrF6. An activation barries of 16.9 kcal/mol is calculated for pseudorotation to a trigonal prism transition structure. CrF5 is found to be dynamically Jahn-Teller distorted from D-3h, to C-2v symmetry.