  Gamma-ray line emission is a direct probe of the nucleosynthesis that occurs
in Type Ia supernovae. In this work we describe the wealth of information
obtainable from observations of this emission. Advanced Compton telescope
designs are being studied by the Naval Research Laboratory, with the goal being
the construction of a telescope which would be capable of detecting SNe Ia to
distances in excess of 100 Mpc. We describe the instrument capabilities and the
design issues that are being addressed. We assume a SN Ia rate and quantify the
frequency at which an advanced Compton telescope could detect, discriminate
between, and diagnose Type Ia supernovae. From these estimates, we argue that
an advanced Compton telescope would be a powerful astrophysical tool.
