The adiabatic theory of tunneling ionization has been successfully used to describe tunneling ionization of atoms [Phys. Rev. A 86, 043417 (2012)]. This theory works particularly well for describing systems in strong, slowly oscillating laser fields in the near and far-infrared parts of the spectrum; a regime of laser parameters that are currently receiving a lot of attention within strong field physics. In this work we seek to apply the adiabatic theory to molecular systems, while treating both nuclear and electronic degrees of freedom. We propose a theory that combines adiabatic theory with a variation of the well known Born-Oppenheimer approximation. The results of this theory is compared to accurate TDSE calculations.