  In this paper we prove a combination theorem for Veech subgroups of the
mapping class group analogous to the first Klein-Maskit combination theorem for
Kleinian groups in which two Fuchsian subgroups are amalgamated along a
parabolic subgroup. As a corollary, we construct subgroups of the mapping class
group (for all genus at least 2), which are isomorphic to non-abelian closed
surface groups in which all but one conjugacy class (up to powers) is
pseudo-Anosov.
