We demonstrate the operation of a two-bit ''controlled-NOT'' quantum l
ogic gate, which, in conjunction with simple single-bit operations, fo
rms a universal quantum logic gate for quantum computation. The two qu
antum bits are stored in the internal and external degrees of freedom
of a single trapped atom, which is first laser cooled to the zero-poin
t energy. Decoherence effects are identified for the operation, and th
e possibility of extending the system to more qubits appears promising
.