  We define a trisection of a closed, orientable three dimensional manifold
into three handlebodies, and a notion of stabilization for these trisections.
Several examples of trisections are described in detail. We define the
trisection genus $t(M)$ of a 3-manifold, and relate it to the Heegaard genus
$g(M)$, showing that $t(M) \le g(M) \le 2t(M)$. We show moreover that the bound
$g(M) \le 2t(M)$ is tight. We define stabilizations of trisections and show
that all trisections of a 3-manifold are stably equivalent, providing an
analogue of the Reidemeister-Singer theorem for trisections. We conclude by
showing that there exist complicated trisections of $S^3$.
