  The Chen groups of a finitely-presented group G are the lower central series
quotients of its maximal metabelian quotient, G/G''. The direct sum of the Chen
groups is a graded Lie algebra, with bracket induced by the group commutator.
If G is the fundamental group of a formal space, we give an analog of a basic
result of D. Sullivan, by showing that the rational Chen Lie algebra of G is
isomorphic to the rational holonomy Lie algebra of G modulo the second derived
subalgebra. Following an idea of W.S. Massey, we point out a connection between
the Alexander invariant of a group G defined by commutator-relators, and its
integral holonomy Lie algebra.
  As an application, we determine the Chen Lie algebras of several classes of
geometrically defined groups, including surface-like groups, fundamental groups
of certain classical link complements, and fundamental groups of complements of
complex hyperplane arrangements. For link groups, we sharpen Massey and
Traldi's solution of the Murasugi conjecture. For arrangement groups, we prove
that the rational Chen Lie algebra is combinatorially determined.
