Accreting carbon-oxygen white dwarfs approaching the Chandrasekhar mass may provide a substantial fraction of Type Ia supernovae. The hydrodynamics of nuclear burning in these models remains uncertain, but all current models are characterized by an initial period of slow, nearly laminar flame propagation at a well-known conductive speed. For cold white dwarfs and slow accretion, the density at the center of the white dwarf at ignition may be quite high, extending perhaps beyond the highest value allowed before accretion-induced collapse occurs, ~9 × 109 g cm-3. The nucleosynthesis that occurs in stars slightly below this critical value, specifically ρc = 2-8 × 109 g cm-3, is explored here using a large nuclear reaction network that allows the resulting abundances of neutron-rich nuclei in the mass range 12-90 to be determined accurately for realistic models of the explosion. It is found that these explosions are responsible for producing the solar abundances of 48Ca, 50Ti, 54Cr, and 70Zn, with appreciable contributions to 58Fe, 64Ni, 66Zn, 76Ge, 82Se, and the gamma-astronomy candidate, 60Fe. Provided a prompt detonation does not occur, these results are insensitive to the physics of flame propagation after the first few hundredths of a solar mass has burned. They are, however, mildly sensitive to the ignition density and uncertain weak interaction rates below Ye ~ 0.42. Since these nuclei, especially 48Ca, cannot be produced anywhere else in nature, the results show that Chandrasekhar mass explosions must occasionally occur (an event rate about 2% of the observed Type Ia supernova rate is estimated for these higher density explosions); however, most Type Ia supernovae must ignite at an appreciably lower density, 2 × 109 g cm-3. Implications for gamma-ray astronomy and meteorite anomalies are briefly discussed.