  We show that, in the heavy quark limit, the hadronic matrix elements that
enter $B$ meson decays into two light mesons can be computed from first
principles, including `non-factorizable' strong interaction corrections, and
expressed in terms of form factors and meson light-cone distribution
amplitudes. The conventional factorization result follows in the limit when
both power corrections in $1/m_b$ and radiative corrections in $\alpha_s$ are
neglected. We compute the order-$\alpha_s$ corrections to the decays
$B_d\to\pi^+\pi^-$, $B_d\to\pi^0\pi^0$ and $B^+\to\pi^+\pi^0$ in the heavy
quark limit and briefly discuss the phenomenological implications for the
branching ratios, strong phases and CP violation.
