We predict that cyanoacetylene (HC₃N) is produced photochemically in the atmosphere of GJ 1132 b in abundances detectable by the James Webb Space Telescope (JWST), assuming that the atmosphere is hydrogen dominated and rich in molecular nitrogen (N₂), methane (CH₄), and hydrogen cyanide (HCN), as described by Swain et al. First, we construct line lists and cross sections for HC₃N. Then we apply these cross sections and the model atmosphere of Swain et al. to a radiative transfer model in order to simulate the transmission spectrum of GJ 1132 b as it would be seen by JWST, accounting for the uncertainty in the retrieved abundances. We predict that cyanoacetylene features at various wavelengths, with a clear lone feature at 4.5 μm, observable by JWST after one transit. This feature persists within the 1σ uncertainty of the retrieved abundances of HCN and CH₄. The signal is detectable for stratospheric temperatures ≲600 K and moderate stratospheric mixing (10⁶ cm² s⁻¹ ≲ K _zz ≲ 10⁸ cm² s⁻¹). Our results also indicate that HC₃N is an important source of opacity that future retrieval models should consider.