  Choreography automata are an automata-based model of choreographies, that we
show to be a compositional one. Choreography automata represent global views of
choreographies (and rely on the well-known model of communicating finite-state
machines to model local behaviours). The projections of well-formed global
views are live as well as lock- and deadlock-free. In the class of choreography
automata we define an internal operation of {\em composition}, which connects
two global views via roles acting as interfaces. We show that under mild
conditions the composition of well-formed choreography automata is well-formed.
The composition operation enables for a flexible modular mechanism at the
design level.
