  The width of a recently discovered excited charmed-strange baryon, a
candidate for a state $\Xi_c^*$ with spin 3/2, is calculated. In the absence of
configuration mixing between the ground-state (spin-1/2) charmed-strange baryon
$\Xi_c^{(a)}$ and the spin-1/2 state $\Xi_c^{(s)}$ lying about 95 MeV above it,
one finds $\tilde \Gamma(\Xi^*_c \to \Xi_c^{(a)} \pi) = (3/4) \tilde
\Gamma(\Xi^* \to \Xi \pi)$ and $\tilde \Gamma(\Xi^*_c \to \Xi_c^{(s)} \pi) =
(1/4) \tilde \Gamma(\Xi^* \to \Xi \pi)$, where the tilde denotes the partial
width with kinematic factors removed. Assuming a kinematic factor for P-wave
decay of $p_{\rm cm}^3$, one predicts $\Gamma(\Xi^*_c \to \Xi_c^{(a)} \pi) =
2.3$ MeV, while the $\Xi^*_c \to \Xi_c^{(s)} \pi$ channel is closed. Some
suggestions are given for detecting the $\Sigma_c^*$, the spin-3/2 charmed
nonstrange baryon, and the $\Omega_c^*$, the spin-3/2 charmed doubly-strange
baryon.
