The strong coupling constant ${\ensuremath{\alpha}}_{s}$ has been determined from a study of the reaction $\overline{p}p\ensuremath{\rightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}X$, $W\ensuremath{\rightarrow}e\ensuremath{\nu}$ at $\sqrt{s}$ of 630 GeV in the UA1 experiment at CERN. The measurement is based upon a study of jet production in association with $W$ bosons. The result obtained is ${\ensuremath{\alpha}}_{s}({M}_{W}^{2})=0.127\ifmmode\pm\else\textpm\fi{}0.026(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.034(\mathrm{syst})$.