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 Λ c ↔ Σ 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.