The presence of unburned material in the ejecta of normal Type Ia supernovae (SNe Ia) is investigated using early-time spectroscopy obtained by the Carnegie Supernova Project. The tell-tale signature of pristine material from a C+O white dwarf progenitor star is the presence of carbon, as oxygen is also a product of carbon burning. The most prominent carbon lines in optical spectra of SNe Ia are expected to arise from CII. We find that at least 30% of the objects in the sample show an absorption at {approx}6300{AA} which is attributed to CII{lambda}6580. An alternative identification of this absorption as H{alpha} is considered to be unlikely. These findings imply a larger incidence of carbon in SNe Ia ejecta than previously noted.