  Random matrix theory has proven very successful in the understanding of the
spectra of chaotic systems. Depending on symmetry with respect to time reversal
and the presence or absence of a spin 1/2 there are three ensembles, the
Gaussian orthogonal (GOE), Gaussian unitary (GUE), and Gaussian symplectic
(GSE) one. With a further particle-antiparticle symmetry the chiral variants of
these ensembles, the chiral orthogonal, unitary, and symplectic ensembles (the
BDI, AIII, and CII in Cartan's notation) appear. A microwave study of the
chiral ensembles is presented using a linear chain of evanescently coupled
dielectric cylindrical resonators. In all cases the predicted repulsion
behavior between positive and negative eigenvalues for energies close to zero
could be verified.
