  Given a flat connection on a manifold with values in a filtered
L-infinity-algebra, we construct a morphism of coalgebras that generalizes the
holonomies of flat connections with values in Lie algebras. The construction is
based on Gugenheim's A-infinity version of de Rham's theorem, which in turn is
based on Chen's iterated integrals. Finally, we discuss examples related to the
geometry of configuration spaces of points in Euclidean space, and to
generalizations of the holonomy representations of braid groups.
