  This paper deals with the existence of solutions of a class of contact mean
field games systems of first order. Cardaliaguet \cite{CAR} found a link
between the weak KAM theory for Hamiltonian systems and mean field games
systems. We prove that there is still a connection between the weak KAM theory
for contact Hamiltonian systems and contact mean field games systems. By the
analysis of properties of the Mather set for contact Hamiltonian systems, we
prove the main existence result.
