A first observation of the rare decay $\eta$ $\to$ ${\mu }^{+}{\mu }^{-}$e${}^{+}$e${}^{-}$ is reported by the CMS Collaboration at the CERN LHC. The result is based on a proton-proton collision data sample at $\sqrt{s}$ = 13.6 TeV corresponding to an integrated luminosity of 38.0 fb${}^{-1}$, acquired in 2022 using a high-rate dimuon trigger. Using the $\eta$ $\to$ ${\mu }^{+}{\mu }^{-}\gamma$ decay channel for normalization, the branching fraction is measured to be $ℬ$($\eta$ $\to$ ${\mu }^{+}{\mu }^{-}$e${}^{+}$e${}^{-}$) = (2.4 $\pm$ 0.8)$\times$ 10${}^{-6}$, with the uncertainty including statistical and systematic sources as well as the $ℬ$($\eta$ $\to$ ${\mu }^{+}{\mu }^{-}\gamma$) uncertainty. This result is about a factor of three smaller than the existing limit, and is consistent with recent theoretical predictions.