  If M is a hyperbolic 3-manifold with a quasigeodesic flow then we show that
\pi_1(M) acts in a natural way on a closed disc by homeomorphisms.
Consequently, such a flow either has a closed orbit or the action on the
boundary circle is M\"obius-like but not conjugate into PSL(2, R). We
conjecture that the latter possibility cannot occur.
