  Metallicity is expected to influence not only the lives of massive stars but
also the outcome of their deaths as supernovae (SNe) and as gamma-ray bursts
(GRBs). However, there are surprisingly few direct measurements of the local
metallicities of different flavors of core-collapse SNe. Here we present the
largest existing set of host-galaxy spectra with H II region emission lines at
the sites of 35 stripped-envelope core-collapse SNe. 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 determinatinos using three
different oxygen-abundance calibrations. The sites of SNe Ic (the demise of the
most heavily stripped stars having lost both the 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 ~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.
