We discuss the effect of possible proximity of a graphite monolayer to the excitonic insulator phase whose origin is shown to be formally analogous to the non-perturbative phenomenon of dynamical chiral symmetry breaking in relativistic theories of 2+1-dimensional Dirac fermions. In the framework of this scenario, we propose a new explanation for the observed linear energy dependence of the quasiparticle damping in layered graphite and predict other potentially observable features associated with this behavior.