  We investigate the distribution of the spacings of adjacent eigenvalues of
the lattice Dirac operator. At zero chemical potential $\mu$, the
nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of
random matrix theory both in the confinement and in the deconfinement phase.
This is indicative of quantum chaos. At nonzero chemical potential, the
eigenvalues of the Dirac operator become complex. We discuss how $P(s)$ can be
defined in the complex plane. Numerical results from an SU(3) simulation with
staggered fermions are compared with predictions from non-hermitian random
matrix theory, and agreement with the Ginibre ensemble is found for $\mu\approx
0.7$.
