  Carbon chain molecules may be an important reservoir of reactive organics
during star and planet formation. Carbon chains have been observed toward
several low-mass young stellar objects (YSOs), but their typical abundances and
chemical relationships in such sources are largely unconstrained. We present a
carbon chain survey toward 16 deeply embedded (Class 0/I) low-mass protostars
made with the IRAM 30 m telescope. Carbon chains are found to be common at this
stage of protostellar evolution. We detect CCS, CCCS, HC$_3$N, HC$_5$N,
l-C$_3$H, and C$_4$H toward 88%, 38%, 75%, 31%, 81%, and 88% of sources,
respectively. Derived column densities for each molecule vary by one to two
orders of magnitude across the sample. As derived from survival analysis,
median column densities range between 1.2$\times 10^{11}$ cm$^{-2}$ (CCCS) and
1.5$\times 10^{13}$ cm$^{-2}$ (C$_4$H) and estimated fractional abundances with
respect to hydrogen range between 2$\times 10^{-13}$ (CCCS) and 5$\times
10^{-11}$ (C$_4$H), which are low compared to cold cloud cores, warm carbon
chain chemistry (WCCC) sources, and protostellar model predictions. We find
significant correlations between molecules of the same carbon chain families,
as well as between the cyanpolyynes (HC$_{\rm n}$N) and the pure hydrocarbon
chains (C$_{\rm n}$H). This latter correlation is explained by a
closely-related production chemistry of C$_{\rm{n}}$H and cyanpolyynes during
low-mass star formation.
