We present ten medium-resolution, high signal-to-noise ratio near-infrared (NIR) spectra of SN 2011fe from SpeX on the NASA Infrared Telescope Facility (IRTF) and Gemini Near-Infrared Spectrograph (GNIRS) on Gemini North, obtained as part of the Carnegie Supernova Project. This data set constitutes the earliest time-series NIR spectroscopy of a Type Ia supernova (SN Ia), with the first spectrum obtained at 2.58 days past the explosion and covering -14.6 to +17.3 days relative to B-band maximum. C I {lambda}1.0693 {mu}m is detected in SN 2011fe with increasing strength up to maximum light. The delay in the onset of the NIR C I line demonstrates its potential to be an effective tracer of unprocessed material. For the first time in a SN Ia, the early rapid decline of the Mg II {lambda}1.0927 {mu}m velocity was observed, and the subsequent velocity is remarkably constant. The Mg II velocity during this constant phase locates the inner edge of carbon burning and probes the conditions under which the transition from deflagration to detonation occurs. We show that the Mg II velocity does not correlate with the optical light-curve decline rate {Delta}m15. The prominent break at ~1.5 {mu}m is the main source of concern for NIR k-correction calculations. We demonstrate here that the feature has a uniform time evolution among SNe Ia, with the flux ratio across the break strongly correlated with {Delta}m15. The predictability of the strength and the onset of this feature suggests that the associated k-correction uncertainties can be minimized with improved spectral templates.
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