Using data recorded by the CLEO-II detector at CESR, we report the first observation of a narrow state decaying into $\Xi_c~+\pi~-$. The state has mass difference $M(\Xi_c~+\pi~-)-M(\Xi_c~+)$ of $178.2\pm0.5\pm1.0$ $\rm{MeV/c~2}$, and a width of $<5.5$ $\rm{MeV/c~2}$ (90\% confidence level limit). The most likely explanation of this new state is that it is the $J=\32$ spin excitation of the $\Xi_c~0$ charmed baryon.
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