Within the chiral constituent quark model of Glozman and Riska, we discuss the stability of heavy pentaquarks, i.e. hadrons containing four light quarks and a heavy antiquark. The spin-dependent part of the Hamiltonian is dominated by the short-range part of the Goldstone-boson-exchange interaction. We find that these systems are not bound, having an energy above the lowest dissociation threshold into a baryon and a meson.