  Extending work of Chen, we prove the Weinstein conjecture in dimension three
for strongly fillable contact structures with either non-vanishing first Chern
class or with strong and exact filling having non-trivial canonical bundle.
This implies the Weinstein conjecture for certain Stein fillable contact
structures obtained by the Eliashberg-Gompf construction.For example we prove
the Weinstein conjecture for the Brieskorn homology spheres $\Sigma(2,3,6n-1)$,
$n\geq2$, oriented as the boundary of the corresponding Milnor fibre.
Furthermore, for tight contact structures on odd lens spaces, non-contractible
closed Reeb orbits are found.
