Metallicity is expected to influence not only the lives of massive stars but also the outcome of their deaths as supernovae (SNe) and gamma-ray bursts (GRBs). However, there are surprisingly few direct measurements of the local metallicities of different flavors of core-collapse SNe (CCSNe). Here, we present the largest existing set of host-galaxy spectra with H II region emission lines at the sites of 35 stripped-envelope CCSNe. We derive local oxygen abundances in a robust manner in order to constrain the SN Ib/c progenitor population. We obtain spectra at the SN sites, include SNe from targeted and untargeted surveys, and perform the abundance determinations using three different oxygen-abundance calibrations. The sites of SNe Ic (the demise of the most heavily stripped stars, having lost both H and He layers) are systematically more metal rich than those of SNe Ib (arising from stars that retained their He layer) in all calibrations. A Kolmogorov-Smirnov test yields the very low probability of 1% that SN Ib and SN Ic environment abundances, which are different on average by åisebox-0.5ex 0.2 dex (in the Pettini & Pagel scale), are drawn from the same parent population. Broad- lined SNe Ic (without GRBs) occur at metallicities between those of SNe Ib and SNe Ic. Lastly, we find that the host-galaxy central oxygen abundance is not a good indicator of the local SN metallicity; hence, large-scale SN surveys need to obtain local abundance measurements in order to quantify the impact of metallicity on stellar death.