We discuss the possibility of significantly enhancing the nonlinear electro-optical response in strained perovskite BaTiO3. First-principles calculations predict the enhancement for both compressive and tensile strain. The physical origin can be traced to strain-induced phonon softening that results in diverging first-order susceptibility. Within the Landau-Ginzburg-Devonshire formalism we demonstrate how, in turn, this divergence results in a diverging second-order susceptibility and Pockels coefficient. Our results suggest a way to optimize BaTiO3 films for use in silicon nanophotonics.