  We study the two-baryon system with two units of charm looking for the
possible existence of a loosely bound state resembling the $H$ dibaryon. We
make use of a chiral constituent quark model tuned in the description of the
baryon and meson spectra as well as the $NN$ interaction. The presence of the
heavy quarks makes the interaction simpler than in light baryon systems. We
analyze possible quark-Pauli effects that would be present in spin-isospin
saturated channels. Our results point to the non-existence of a charmed
$H$-like dibaryon, although it may appear as a resonance above the
$\Lambda_c\Lambda_c$ threshold.
