  In the last few years, the supersymmetry method was generalized to
real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from
ensembles invariant under the orthogonal, unitary, and unitary symplectic
group, respectively. We extend this supersymmetry approach to chiral random
matrix theory invariant under the three chiral unitary groups in a unifying
way. Thereby we generalize a projection formula providing a direct link and,
hence, a `short cut' between the probability density in ordinary space and the
one in superspace. We emphasize that this point was one of the main problems
and critiques of the supersymmetry method since only implicit dualities between
ordinary and superspace were known before. As examples we apply this approach
to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy)
ensemble and an ensemble with a quartic potential. Moreover we consider the
partially quenched partition function of the three chiral Gaussian ensembles
corresponding to four-dimensional continuum QCD. We identify a natural
splitting of the chiral Lagrangian in its lowest order into a part of the
physical mesons and a part associated to source terms generating the
observables, e.g. the level density of the Dirac operator.
