  We construct a Borcherds Kac-Moody (BKM) superalgebra on which the Conway
group Co$_0$ acts faithfully. We show that the BKM algebra is generated by the
BRST-closed states in a chiral superstring theory. We use this construction to
produce denominator identities for the chiral partition functions of the Conway
module $V^{s\natural}$, a supersymmetric $c=12$ chiral conformal field theory
whose (twisted) partition functions enjoy moonshine properties and which has
automorphism group isomorphic to Co$_0$. In particular, these functions satisfy
a genus zero property analogous to that of monstrous moonshine. Finally, we
suggest how one may promote the denominators to spacetime BPS indices in type
II string theory, which might thus furnish a physical explanation of the genus
zero property of Conway moonshine.
