  By solving exact three-body equations, we study the three-baryon system with
charm $+1$. We look for possible bound states using baryon-baryon interactions
obtained from a chiral constituent quark model. The smaller effect of the
$\Lambda_c \leftrightarrow \Sigma_c$ conversion reverses the order of the
$(I,J)=(0,1/2)$ and $(I,J)=(0,3/2)$ states, rather close on the strange sector.
The diminishing of the kinetic energy due to the large reduced mass gives rise
to a bound state in the $(I,J)=(0,3/2)$ channel. After correcting for Coulomb
effects the binding energy would be between 140 and 715 keV.
