  We construct a self-dual integral form of the moonshine vertex operator
algebra, and show that it has symmetries given by the Fischer-Griess monster
simple group. The existence of this form resolves the last remaining open
assumption in the proof of the modular moonshine conjecture by Borcherds and
Ryba. As a corollary, we find that Griess's original 196884-dimensional
representation of the monster admits a positive-definite self-dual integral
form with monster symmetry.
