Recent progress on micro- and nanometer-scale manipulation has opened the possibility to probe systems small enough that thermal fluctuations of energy and coordinate variables can be significant compared with their mean behavior. We present an experimental study of nonequilibrium thermodynamics in a classical two-state system, namely, a metallic single-electron box. We have measured with high statistical accuracy the distribution of dissipated energy as single electrons are transferred between the box electrodes. The obtained distributions obey Jarzynski and Crooks fluctuation relations. A comprehensive microscopic theory exists for the system, enabling the experimental distributions to be reproduced without fitting parameters.