We study the electronic band structure for a model one-dimensional per
iodic potential in the presence of a spatially homogeneous laser field
. The statistical properties of the energy bands depend on the couplin
g between the crystal and the laser field, going from Poisson to Wigne
r-Dyson (GOE) and back to Poisson as the coupling increases. We argue
that the classical dynamics of this system resembles that of a periodi
cally driven pendulum. We find that the chaotic regime is not restrict
ed solely to high-lying bands and should thus be of easier access to o
ptical experiments.