A second order Møller-Plesset perturbation theory which is free of the basis set superposition error (BSSE) is developed based on the "Chemical Hamiltonian Approach" (CHA). The zeroth order Hamiltonian is built up on the BSSE-free (but not orthogonal and not necessarily real) canonic CHA-SCF orbitals and their orbital energies. As the exclusion of BSSE makes the problem nonHermitian, biorthogonal perturbation theory is used to obtain the first order wave function. The second order energy is, however, calculated by using the conventional Hermitian Hamiltonian, in accord with the "CHA with conventional energy" recipe. For that reason we use a generalized Hylleraas functional introduced recently; this guarantees the second order energy to be real even in the case of complex CHA-SCF orbitals. The matrix elements entering the generalized Hylleraas functional are calculated by transforming all wave functions, creation and annihilation operators to an auxiliary orthonormalized basis. The new CHA-MP2 method has been tested on a number of van der Waals complexes and hydrogen bonded systems, by using a variety of different basis sets. In all cases a remarkable agreement has been found with the results given by the Boys and Bernardi's counterpoise method (CP); this agreement is especially striking in the case of large and well-balanced basis sets. This indicates that the conceptually different CHA and CP schemes both take into account correctly the major BSSE effects.