We have observed the decay ${B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{0}{K}^{+}$, using $3.3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected with the CLEO II detector at the Cornell Electron Storage Ring. We find the ratio of branching fractions $R\ensuremath{\equiv}B({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{0}{K}^{+})/B({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{0}{\ensuremath{\pi}}^{+})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.055\ifmmode\pm\else\textpm\fi{}0.014\ifmmode\pm\else\textpm\fi{}0.005$.