We present 75 near-infrared (NIR; 0.8-2.5 μm) spectra of 34 stripped-envelope core-collapse supernovae (SESNe) obtained by the Carnegie Supernova Project-II (CSP-II), encompassing optical spectroscopic Types IIb, Ib, Ic, and Ic-BL. The spectra range in phase from pre-maximum to 80 days past maximum. This unique data set constitutes the largest NIR spectroscopic sample of SESNe to date. NIR spectroscopy provides observables with additional information that is not available in the optical. Specifically, the NIR contains the strong lines of He i and allows a more detailed look at whether Type Ic supernovae are completely stripped of their outer He layer. The NIR spectra of SESNe have broad similarities, but closer examination through statistical means reveals a strong dichotomy between NIR "He-rich"and "He-poor"SNe. These NIR subgroups correspond almost perfectly to the optical IIb/Ib and Ic/Ic-BL types, respectively. The largest difference between the two groups is observed in the 2 μm region, near the He i λ2.0581 μm line. The division between the two groups is not an arbitrary one along a continuous sequence. Early spectra of He-rich SESNe show much stronger He i λ2.0581 μm absorption compared to the He-poor group, but with a wide range of profile shapes. The same line also provides evidence for trace amounts of He in half of our SNe in the He-poor group.