  We proceed to the first study of $\eta_c'$ prompt hadroproduction at
next-to-leading order in $\alpha_s$. Based on heavy-quark-spin symmetry, which
is systematically used in quarkonium-production phenomenology, we demonstrate
that prompt $\eta_c'$ can be studied at the LHC with the existing data. We
emphasize its relevance to constrain $\psi'$ production, in the same way as the
first prompt $\eta_c'$ data at the LHC lately strongly impacted the
phenomenology of $J/\psi$ studies.
