Abstract : The nearby Type Ia supernova SN 2011fe in M101 (cz=241 km s^-1) provides a unique opportunity to study the early evolution of a "normal" Type Ia supernova, its compositional structure, and its elusive progenitor system. We present 18 high signal-to-noise spectra of SN 2011fe during its first month beginning 1.2 days post-explosion and with an average cadence of 1.8 days. This gives a clear picture of how various line-forming species are distributed within the outer layers of the ejecta, including that of unburned material (C+O). We follow the evolution of C II absorption features until they diminish near maximum light, showing overlapping regions of burned and unburned material between ejection velocities of 10,000 and 16,000 km s^-1. This supports the notion that incomplete burning, in addition to progenitor scenarios, is a relevant source of spectroscopic diversity among SNe Ia. The observed evolution of the highly Doppler-shifted O I 7774 absorption features detected within five days post-explosion indicate the presence of O I with expansion velocities from 11,500 to 21,000 km s^-1. The fact that some O I is present above C II suggests that SN 2011fe may have had an appreciable amount of unburned oxygen within the outer layers of the ejecta.