Observations of chemical species can provide an insight into the physical conditions of the emitting gas but it is important to understand how their abundances and excitation vary within different heating environments. C$_2$H is a molecule typically found in PDR regions of our own Galaxy but there is evidence to suggest it also traces other regions undergoing energetic processing in extragalactic environments. As part of the ALCHEMI ALMA large program, the emission of C$_2$H in the central molecular zone of the nearby starburst galaxy NGC 253 was mapped at 1.6 (28 pc) resolution and characterized to understand its chemical origins. Spectral modelling of the N=1-0 through N=4-3 rotational transitions of C$_2$H was used to derive the C$_2$H column densities towards the dense clouds in NGC 253. Chemical modelling, including PDR, dense cloud, and shock models were then used to investigate the chemical processes and physical conditions that are producing the molecular emission. We find high C$_2$H column densities of $sim 10^{15} cm^{-3}$ detected towards the dense regions of NGC 253. We further find that these column densities cannot be reproduced by assuming that the emission arises from the PDR regions at the edge of the clouds. Instead, we find that the C$_2$H abundance remains high even in the high visual extinction interior of these clouds and that this is most likely caused by a high cosmic-ray ionization rate.