  Let G be a chordal graph, X(G) the complement of the associated complex
arrangement and Gamma(G) the fundamental group of X(G). We show that Gamma(G)
is a limit of colored braid groups over the poset of simplices of G. When G =
G_T is the comparability graph associated with a rooted tree T, a case recently
investigated by the first author, the result takes the following very simple
form: Gamma(G_T) is a limit over T of colored braid groups.
