We discuss the effect of the 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, such as weak ferromagnetism at low doping.