We examine the feasibility of a parity non-conserving (PNC) optical rotation experiment for the 2 P 3/2 → 2 P 1/2 transition of atomic iodine at 1315 nm. The calculated E1PNC to M 1 amplitude ratio is R = 0.80(16) × 10 −8 . We show that very large PNC rotations (greater than 10 µrad) are obtained for iodine-atom column densities of ∼ 10 22 cm −2 , which can be produced by increasing the effective interaction pathlength by a factor of ∼ 10 4 with a high-finesse optical cavity. The simulated signals indicate that measurement of the nuclear anapole moment is feasible, and that a 1% PNC precision measurement should resolve the inconsistency between previous measurements in Cs and Tl. [5][6][7][8]. The highlight of these efforts was the 0.35% precision measurement of nuclear-spin-independent PNC in Cs, and the 14% precision measurement of the nuclear spin-dependent PNC for the odd-proton nucleus of 133 Cs [4]. However, measurement of the anapole moment in Cs disagrees with Tl [4,5], and also with some theoretical nuclear calculations ([9-11] and references therein). To help resolve these inconsistencies, and to improve the atomic PNC tests of the standard model, further experiments are needed. For example, there is a proposal to measure the nuclear anapole moment using the PNC-generated hyperfine frequency shift of dressed states in atoms [12], with particular proposals for Cs [13] and Fr [14]. However, for other PNC candidates, as the precision in the atomic theory is not expected to significantly surpass the current experimental or theoretical PNC precision of Cs, future PNC experiments have focused on other fruitful directions, such as the measurement of atomic PNC on a chain of isotopes [9,15], or the measurement of nuclear anapole moments. Therefore, along these lines, PNC experiments are in progress on Yb and Dy at Berkeley [16,17], on Rb and Fr at the Tri-University Meson Facility (TRIUMF, University of British Columbia) [18,19], on Ra + at KVI Groningen [20], and on Ba + at the University of Washington, Seattle [21]. Recently, Bougas et al.