We present four spectra of the Type Ia supernova SN Ia 2006D extending from -7 to +13 days with respect to B-band maximum. The spectra include the strongest signature of unburned material at photospheric velocities observed in a SN Ia to date. The earliest spectrum exhibits C II absorption features below 14,000 km/s, including a distinctive C II lambda 6580 absorption feature. The carbon signatures dissipate as the SN approaches peak brightness. In addition to discussing implications of photospheric-velocity carbon for white dwarf explosion models, we outline some factors that may influence the frequency of its detection before and around peak brightness. Two effects are explored in this regard, including depopulation of the C II optical levels by non-LTE effects, and line-of-sight effects resulting from a clumpy distribution of unburned material with low volume-filling factor.