We observe a signal for the doubly charmed baryon ${\ensuremath{\Xi}}_{cc}^{+}$ in the charged decay mode ${\ensuremath{\Xi}}_{cc}^{+}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ in data from SELEX, the charm hadroproduction experiment at Fermilab. We observe an excess of 15.9 events over an expected background of $6.1\ifmmode\pm\else\textpm\fi{}0.5$ events, a statistical significance of $6.3\ensuremath{\sigma}$. The observed mass of this state is $3519\ifmmode\pm\else\textpm\fi{}1\text{ }\text{ }\mathrm{M}\mathrm{e}\mathrm{V}/{c}^{2}$. The Gaussian mass width of this state is $3\text{ }\text{ }\mathrm{M}\mathrm{e}\mathrm{V}/{c}^{2}$, consistent with resolution; its lifetime is less than 33 fs at 90% confidence.