The optical hybridization of the electronic states in strongly coupled molecule-cavity systems have revealed unique properties, such as lasing, room temperature polariton condensation and the modification of excited electronic landscapes involved in molecular isomerization. Here we show that molecular vibrational modes of the electronic ground state can also be coherently coupled with a microcavity mode at room temperature, given the low vibrational thermal occupation factors associated with molecular vibrations, and the collective coupling of a large ensemble of molecules immersed within the cavity-mode volume. This enables the enhancement of the collective Rabi-exchange rate with respect to the single-oscillator coupling strength. The possibility of inducing large shifts in the vibrational frequency of selected molecular bonds should have immediate consequences for chemistry.