A novel approach for calculating nuclear wave functions and energies of He-3 clusters doped with an atomic or molecular impurity is developed. It adopts the systematic and well developed methodology of quantum chemistry employing an analogy between electrons bound by Coulomb forces to the nuclei and fermionic He-3 atoms clustered around a dopant species. The differences primarily concern the different shapes of the helium-helium and helium-impurity potentials and the larger mass of the He-3 atom, as compared to electronic structure problems. A new integral evaluation procedure is outlined, as well as the necessary modifications to electronic structure codes. Tests against numerically exact calculations for Imp-He-3 (Imp=Ne, Ar, Kr, Xe, and SF6) complexes show that a modest set of 15 basis functions provides accurate and converged results. Calculations for the lowest triplet state of the SF6(He-3)(2) cluster, where fermionic statistics comes into play in the orbital part of the helium nuclear wave function, are presented. The triplet state is bound by 22 mu hartree with respect to dissociation into He-3+SF6-He-3. The applicability of the new method to larger systems is discussed.