For the first time, a search for the rare decay of the $W$ boson to three charged pions has been performed. Proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $77.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, have been analyzed. No significant excess is observed above the background expectation. An upper limit of $1.01\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ is set at 95% confidence level on the branching fraction of the $W$ boson to three charged pions. This provides a strong motivation for theoretical calculations of this branching fraction.