  The chiral SU(3) Lagrangian with pseudoscalar and vector $D$ mesons and with
the octet and decuplet baryons is considered. The leading two-body counter
terms involving two baryon fields and two $D$ meson fields are constructed in
the open-charm sector. There are 26 terms. A combined expansion in the inverse
of the charm quark mass and in the inverse of the number of colors provides sum
rules that reduce the number of free parameter down to 5 only. Our result shows
the feasibility of a systematic computation of the open-charm baryon spectrum
based on coupled-channel dynamics.
