  A symplectic integrator algorithm suitable for hierarchical triple systems is
formulated and tested. The positions of the stars are followed in hierarchical
Jacobi coordinates, whilst the planets are referenced purely to their primary.
The algorithm is fast, accurate and easily generalised to incorporate
collisions. There are five distinct cases -- circumtriple orbits, circumbinary
orbits and circumstellar orbits around each of the stars in the hierarchical
triple -- which require a different formulation of the symplectic integration
algorithm. As an application, a survey of the stability zones for planets in
hierarchical triples is presented, with the case of a single planet orbiting
the inner binary considered in detail. Fits to the inner and outer edges of the
stability zone are computed. Considering the hierarchical triple as two
decoupled binary systems, the earlier work of Holman & Wiegert on binaries is
shown to be applicable to triples, except in the cases of high eccentricities
and close or massive stars. Application to triple stars with good data in the
multiple star catalogue suggests that more than 50 per cent are unable to
support circumbinary planets, as the stable zone is almost non-existent.
