  Large ensembles of complete spectra of the Euclidean Dirac operator for
staggered fermions are calculated for SU(2) lattice gauge theory. The
accumulation of eigenvalues near zero is analyzed as a signal of chiral
symmetry breaking and compared with parameter-free predictions from chiral
random matrix theory. Excellent agreement for the distribution of the smallest
eigenvalue and the microscopic spectral density is found. This provides direct
evidence for the conjecture that these quantities are universal functions.
