Atomic Parity Violation provides the rare opportunity of a low energy window into possible new fundamental processes at very high mass scales normally investigated at large high energy accelerators. Precise measurements on atomic systems are currently the most sensitive probes of many kinds of new physics, and complement high energy experiments. Present atomic experiments are beginning to reach their limits of precision due to either sensitivity, systematics or atomic structure uncertainties. An experiment in a single trapped Barium ion can improve on all of these difficulties. This experiment uses methods to precisely manipulate and detect the spin state of a single ion in order to measure a parity induced splitting of the ground state magnetic sublevels in externally applied laser fields. The same methods can be used to provide precise measurements of more conventional atomic structure parameters.