  We show that the substitutional vacancy in graphene forms a dynamical
Jahn-Teller center. The adiabatic potential surface resulting from the
electron-lattice coupling was computed using density-functional methods and
subsequently the Schr\"odinger equation was solved for the nuclear motion. Our
calculations show a large tunnelling splitting $3 \Gamma$ of about 86
cm$^{-1}$. %, which is large as compared to the typical strain splitting. The
effect results in a large delocalization of the carbon nuclear wave functions
around the vacancy leading to a significant broadening of the Jahn-Teller
active $sp^2\sigma$ electron states. The tunnelling splitting should be
observable in electron paramagnetic resonance and two-photon resonance
scattering experiments.
