  We discuss a new method to determine the low-energy couplings of the $\Delta
S=1$ weak Hamiltonian in the $\epsilon$-regime. It relies on a matching of the
topological poles in $1/m^2$ of three-point functions of two pseudoscalar
densities and a four-fermion operator computed in lattice QCD, to the same
observables in the Chiral Effective Theory. We present the results of a NLO
computation in chiral perturbation theory of these correlation functions
together with some preliminary numerical results.
