  We present 75 near-infrared (NIR; 0.8$-$2.5 $\mu$m) 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 resonance 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 $\mu$m region, near the He I $\lambda$2.0581 $\mu$m
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
$\lambda$2.0581 $\mu$m 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.
