  Using data recorded by the CLEO II detector at CESR, we report evidence for
two new charmed baryons, one decaying into $\Xi_c^+\pi^+\pi^-$ via an
intermediate $\Xi_c^{*0}$, and its isospin partner decaying into
$\Xi_c^0\pi^+\pi^-$ via an intermediate $\Xi_c^{*+}$. We measure the mass
differences of the two states to be $M(\Xi_c^+\pi^+\pi^-)-M(\Xi_c^+)=$
$348.6\pm0.6\pm1.0$ MeV, and $M(\Xi_c^0\pi^+\pi^-)-M(\Xi_c^0)=$
$347.2\pm0.7\pm2.0$ MeV. We interpret these new states as the $J^P = {3
\over{2}}^- $ $\Xi_{c1}$ particles, the charmed-strange analogues of the
$\Lambda_{c1}^+(2625)$.
