  We study complete eigenvalue spectra of the staggered Dirac matrix in
quenched QCD on a $6^3\times 4$ lattice. In particular, we investigate the
nearest-neighbor spacing distribution $P(s)$ for various values of $\beta$ both
in the confinement and deconfinement phase. In both phases except far into the
deconfinement region, the data agree with the Wigner surmise of random matrix
theory which is indicative of quantum chaos. No signs of a transition to
Poisson regularity are found, and the reasons for this result are discussed.
