  We investigate the crystal structure and the electronic properties of the
trilayer nickelate La$_4$Ni$_3$O$_{10}$ by means of quantum mechanical
calculations in the framework of the density functional theory. We find that,
at low temperature, La$_4$Ni$_3$O$_{10}$ undergoes a hitherto unreported
structural phase transition and transforms to a new monoclinic $P2_1/a$ phase.
This phase exhibits electronic properties in agreement with recent
angle-resolved photoemission spectroscopy data reported in H.\ Li \emph{et
al}., Nat.\ Commun.\ \textbf{8}, 704 (2017) and should be considered in models
focused on explaining the observed $\sim$140\,K metal-to-metal phase
transition.
