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We present the first lattice QCD calculation of the leading-ordermomentum-independent parity violating coupling between pions and nucleons,$h_{\pi{NN}}^1$. The calculation performs measurements on dynamical anisotropicclover gauge configurations, with a spatial extent of $L\sim2.5$ fm, a spatiallattice spacing of $a_s\sim0.123$ fm, and a pion mass of $m_{\pi}\sim389$ MeV.While this first calculation does not include non-perturbative renormalizationof the bare parity-violating operators, a chiral extrapolation to the physicalpion mass, or contributions from disconnected (quark-loop) diagrams, these areexpected to result in systematic errors within the quoted statistical error. Wefind a contribution from the `connected' diagrams of$h_{\pi{NN}}^{1,con}=(1.099\pm0.505^{+0.058}_{-0.064})\times10^{-7}$,consistent with current experimental bounds and previous model-dependenttheoretical predictions.

Lattice QCD Calculation of Nuclear Parity Violation