A key tracer of galaxy evolution is to look at how the chemical compositions of galaxies have changed over time. After oxygen, which is an important tracer of metallicity, carbon plays the largest role in the chemical evolution of galaxies. Relative C and O abundances can be used to constrain the star formation histories of individual galaxies and the time evolution of CNO abundances is necessary to properly model stellar isochrones, yet our knowledge of the relative C and O abundances in other galaxies has not advanced significantly in the last 25 years. To address this issue, we obtained new UV spectra for nearby, low-metallicity, high-ionization dwarf galaxies using HST/COS. With these data we established the first analysis of C/O in local galaxies based solely on simultaneous significant detections of the UV O+2 and C+2 collisionally excited lines. We find that at low metallicity, (12+log(O/H) < 8.0), no clear trend is evident in C/O versus O/H given the large dispersion observed. When combined with recombination line observations at higher values of O/H, a general trend of increasing C/O with increasing O/H is also viable but with some significant outliers. Additionally, we find the C/N ratio appears to be constant (but with significant scatter) over a large range in oxygen abundance, indicating that carbon is predominantly produced by similar nucleosynthetic mechanisms as nitrogen. If true, and our current understanding of nitrogen production is correct, this would indicate that primary production of carbon (a flat trend) dominates at low metallicity, but quasi- secondary production (an increasing trend) becomes prominent at higher metallicities.