  Given a compact Kaehler manifold, we consider the complement U of a divisor
with normal crossings and a unitary local system V on it. We consider a
differential graded Lie algebra (DGLA) of forms with holomorphic logarithmic
singularities and vanishing residues. We construct a spectral sequence
corresponding to the anti-holomorphic filtration of this algebra and compute
its E1 term. This spectral sequence converges to the L2 cohomology H2*(U, V).
We show that this DGLA is formal, although it does not always satisfy to the
d'd''-Lemma.
