  We show that any smooth, closed, oriented, connected 4--manifold can be
trisected into three copies of $\natural^k (S^1 \times B^3)$, intersecting
pairwise in 3--dimensional handlebodies, with triple intersection a closed
2--dimensional surface. Such a trisection is unique up to a natural
stabilization operation. This is analogous to the existence, and uniqueness up
to stabilization, of Heegaard splittings of 3--manifolds. A trisection of a
4--manifold $X$ arises from a Morse 2--function $G:X \to B^2$ and the obvious
trisection of $B^2$, in much the same way that a Heegaard splitting of a
3--manifold $Y$ arises from a Morse function $g : Y \to B^1$ and the obvious
bisection of $B^1$.
