  We predict that cyanoacetylene (HC$_3$N) 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 (N$_2$), methane (CH$_4$) and hydrogen cyanide (HCN), as
described by Swain et al. (2021). First, we construct line list and
cross-sections for HC$_3$N. Then we apply these cross-sections and the model
atmosphere of Swain et al. (2021) 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 $\mu$m, observable by JWST after one transit. This feature persists within
the $1-\sigma$ uncertainty of the retrieved abundances of HCN and CH$_4$. The
signal is detectable for stratospheric temperatures $\lesssim 600$ K and
moderate stratospheric mixing ($10^6 \, {\rm cm^2 \, s^{-1}} \lesssim K_{zz}
\lesssim 10^8 \, {\rm cm^2 \, s^{-1}}$). Our results also indicate that HC$_3$N
is an important source of opacity that future retrieval models should consider.
