  We use a G2-structure on a 7-dimensional Riemannian manifold with a fixed
metric to define an octonion bundle with a fiberwise non-associative product.
We then define a metric-compatible octonion covariant derivative on this bundle
that is compatible with the octonion product. The torsion of the G2-structure
is then shown to be an octonionic connection for this covariant derivative with
curvature given by the component of the Riemann curvature that lies in the
7-dimensional representation of G2. We also interpret the choice of a
particular G2-structure within the same metric class as a choice of gauge and
show that under a change of this gauge, the torsion does transform as an
octonion-valued connection 1-form. Finally, we also show an explicit
relationship between the octonion bundle and the spinor bundle, define an
octonionic Dirac operator and explore an energy functional for octonion
sections. We then prove that critical points correspond to divergence-free
torsion, which is shown to be an octonionic analog of the Coulomb gauge.
