  We propose an implementation of an universal quantum cloning machine [UQCM,
Hillery and Buzek, Phys. Rev. A {\bf 56}, 3446 (1997)] in a Cavity Quantum
Electrodynamics (CQED) experiment. This UQCM acts on the electronic states of
atoms that interact with the electromagnetic field of a high $Q$ cavity. We
discuss here the specific case of the $1 \to 2$ cloning process using either a
one- or a two-cavity configuration.
