  The systolic ratio of a contact form on a closed three-manifold is the
quotient of the square of the shortest period of closed Reeb orbits by the
contact volume. We show that every co-orientable contact structure on any
closed three-manifold is defined by a contact form with arbitrarily large
systolic ratio. This shows that the many existing systolic inequalities in
Finsler and Riemannian geometry are not purely contact-topological phenomena.
