The presence of strong He I absorption troughs in the optical spectra of Type Ib SNs is attributed to non-thermal excitation. As for analogous effects in the premaximum spectra of SN 1987A, the early importance of nonthermal excitation in the Ib's is fundamentally due to a large-scale instability that mixes Ni-56 out into their envelopes shortly after explosion. Because of this mixing, the helium-rich envelopes of these SNs are, even at maximum light, not strongly shielded from the gamma-rays emitted by Co-56 nuclei. In consequence, the helium atoms are subject to impact excitations and ionizations by the nonthermal electrons in the cascades created in the stopping of the MeV Compton electrons produced in the scattering of these gamma-rays. A non-LTE treatment of this nonthermal excitation of helium is given using a recent model of a Type Ib SN due to Shigeyama et al. that invokes mixing of Ni-56 in order to reproduce observed light curves. The statistical equilibrium calculations predict gross overpopulations of the n = 2 levels, in qualitative agreement with those inferred empirically by Harkness et al., and the resulting theoretical spectra show encouraging agreement with observation. The possible relevance of these calculations to the differences in spectra and light curves between the Ib's and the Ia's and Ic's is briefly discussed.