Sire study complete eigenvalue spectra of the staggered Dirac matrix i
n quenched QCD on a 6(3) x 4 lattice. In particular, we investigate th
e nearest-neighbor spacing distribution P(s) for various values of bet
a both in the confinement and deconfinement phase. In both phases exce
pt far into the deconfinement region, the data agree with the Wigner s
urmise of random matrix theory which is indicative of quantum chaos. N
o signs of a transition to Poisson regularity are found, and the reaso
ns for this result are discussed.