Motivated by recent photodetachment experiments studying resonance structures in the transition-state region of the F + CH4 -> HF + CH3 reaction, the vibrational dynamics of the precursor complex CH4 center dot F- is investigated. Delocalized vibrational eigenstates of CH4 center dot F- are computed in full dimensionality employing the multiconfigurational time-dependent Hartree (MCTDH) approach and a recently developed iterative diagonalization approach for general multiwell systems. Different types of stereographic coordinates are used, and a corresponding general. N-body kinetic energy operator is given. The calculated tunneling splittings of the ground and the lower vibrational excited states of the CH4 center dot F- complex do not significantly exceed 1 cm(-1). Comparing the converged MCTDH results for localized vibrational excitations with existing results obtained by normal-mode-based (truncated) vibrational configuration interaction calculations Significantly lower frequencies. are found for excitations in the intermolecular,modes.