  Let $\{T^t\}$ be a smooth flow with positive speed and positive topological
entropy on a compact smooth three dimensional manifold, and let $\mu$ be an
ergodic measure of maximal entropy. We show that either $\{T^t\}$ is Bernoulli,
or $\{T^t\}$ is isomorphic to the product of a Bernoulli flow and a rotational
flow. Applications are given to Reeb flows.
