  To a plane algebraic curve of degree n, Moishezon associated a braid
monodromy homomorphism from a finitely generated free group to Artin's braid
group B_n. Using Hansen's polynomial covering space theory, we give a new
interpretation of this construction. Next, we provide an explicit description
of the braid monodromy of an arrangement of complex affine hyperplanes, by
means of an associated ``braided wiring diagram.'' The ensuing presentation of
the fundamental group of the complement is shown to be Tietze-I equivalent to
the Randell-Arvola presentation. Work of Libgober then implies that the
complement of a line arrangement is homotopy equivalent to the 2-complex
modeled on either of these presentations. Finally, we prove that the braid
monodromy of a line arrangement determines the intersection lattice. Examples
of Falk then show that the braid monodromy carries more information than the
group of the complement, thereby answering a question of Libgober.
