We report results from a study of heavy-baryon spectroscopy within a relativistic constituent- quark model, whose hyperfine interaction is based on Goldstone-boson-exchange dynamics. While for light-flavor constituent quarks it is now commonly accepted that the effective quark-quark interaction is (predominantly) furnished by Goldstone-boson exchange - due to spontaneous chiral-symmetry breaking of quantum chromodynamics at low energies - there is currently still much speculation about the light-heavy and heavy-heavy quark-quark interactions. With the increasing amount of experimental data on heavy-baryon spectroscopy these issues might soon be settled. Here, we show, how the relativistic constituent-quark model with Goldstone-boson-exchange hyperfine interactions can be extended to charm and bottom baryons. It is found that the same model that has previously been successful in reproducing the light and strange baryon spectra is also in line with the existing phenomenological data on heavy-baryon spectroscopy. An analogous model with one-gluon-exchange hyperfine interactions for light-heavy flavors does not achieve a similarly good performance.