A novel approach for calculating nuclear wavefunctions and energies of
^3He 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 $^3$He 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
^3He 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-^3He 
(Imp = Ne, Ar, Kr, Xe, and SF_6) complexes show that a modest set of
15 basis functions provides accurate and converged results.
Calculations for the lowest
triplet state of the SF_6(^3He)_2 cluster, where
fermionic statistics comes into play in the orbital part of the helium
nuclear wavefunction, are presented. The triplet state is bound by
22 microhartree with respect to dissociation into ^3He + SF_6-^3He.
The applicability of the new method to larger systems
is discussed.