In this paper, we study the cobordism spectrum $\MO{8}$ at the prime $3$.
This spectrum is important because it is conjectured to play the role
for elliptic cohomology that Spin cobordism plays for real K-theory. 
We show that the torsion is all killed by $3$, and that the
Adams-Novikov spectral sequence collapses after only $2$ differentials.
Many of our methods apply more generally.