  We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3)
gauge theory and in full QCD on a $6^3\times 4$ lattice. As a measure of the
fluctuation properties of the eigenvalues, we study the nearest-neighbor
spacing distribution $P(s)$ for various values of $\beta$ both in the
confinement and in the deconfinement phase. In both phases except far into the
deconfinement region, the lattice data agree with the Wigner surmise of
random-matrix theory which is indicative of quantum chaos. We do not find signs
of a transition to Poisson regularity at the deconfinement phase transition.
