We present the first search for an electrically charged resonance ${W}^{\ensuremath{'}}$ decaying to a $WZ$ boson pair using $4.1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected with the D0 detector at the Fermilab Tevatron $p\overline{p}$ collider. The $WZ$ pairs are reconstructed through their decays into three charged leptons ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$). A total of 9 data events is observed in good agreement with the background prediction. We set 95% C.L. limits on the ${W}^{\ensuremath{'}}WZ$ coupling and on the ${W}^{\ensuremath{'}}$ production cross section multiplied by the branching fractions. We also exclude ${W}^{\ensuremath{'}}$ masses between 188 and 520 GeV within a simple extension of the standard model and set the most restrictive limits to date on low-scale technicolor models.