Antidot arrays consisting of a lattice of nanometer scale holes etched through a two- dimensional electron gas display distinct resistance anomalies which reflect the complex electron motion in the lattice. While in conventional conductors the electrons are scattered by randomly distributed scatterers the situation is different in antidot arrays: here, the electrons predominantly collide with the periodically arranged antidots. The electrons in the lattice probe a potential landscape which can be viewed as a physical realization of a Sinai type of billiard, known for its chaotic classical dynamics.