We propose a new solution to the cosmological constant problem building on a nonperturbative quantum theory of gravity with torsional instantons. These pseudoparticles, which were recently found to exist in a first order formulation of Giddings-Strominger axionic gravity, carry nontrivial Nieh-Yan topological charge. The nonperturbative ground state as generated due to tunneling effects is shown to be stable under quantum fluctuations. Within this framework, the associated vacuum angle, namely the Barbero-Immirzi topological parameter, gets fixed to a numerical value determined by the Hubble constant. * sandipan@iucaa.ernet.in