Two-loop QCD correction to differential semi-leptonic b --> u decays in the shape-function region

We calculate the two-loop QCD correction to the form factors of on-shell b-quark decay to an energetic massless quark, which constitutes the last missing piece required for an O(alpha_s^2) determination of |V_ub| from inclusive semi-leptonic bar B --> X_u l nu decays in the shape-function region.