  Templates are branched 2-manifolds with semi-flows used to model `chaotic'
hyperbolic invariant sets of flows on 3-manifolds. Knotted orbits on a template
correspond to those in the original flow. Birman and Williams conjectured that
for any given template the number of prime factors of the knots realized would
be bounded. We prove a special case when the template is positive; the general
case is now known to be false.
