  Most of the leading explosion scenarios for Type Ia supernovae involve the
nuclear incineration of a white dwarf star through a detonation wave. Several
scenarios have been proposed as to how this detonation may actually occur, but
the exact mechanism and environment in which it takes place remain unknown. We
explore the effects of an off-center initiated detonation on the spatial
distribution of the nucleosynthetic yield products in a toy model -- a
pre-expanded near Chandrasekhar-mass white dwarf. We find that a single-point
near edge-lit detonation results in asymmetries in the density and thermal
profiles, notably the expansion timescale, throughout the supernova ejecta. We
demonstrate that this asymmetry of the thermodynamic trajectories should be
common to off-center detonations where a small amount of the star is burned
prior to detonation. The sensitivity of the yields on the expansion timescale
results in an asymmetric distribution of the elements synthesized as reaction
products. We tabulate the shift in the center of mass of the various elements
produced in our model supernova and find an odd-even pattern for elements past
silicon. Our calculations show that off-center single-point detonations in
carbon-oxygen white dwarfs are marked by significant composition asymmetries in
their remnants which bear potentially observable signatures in both velocity
and coordinate space, including an elemental nickel mass fraction which varies
by a factor of two to three from one side of the remnant to the other.
