  We present the first lattice QCD calculation of the leading-order
momentum-independent parity violating coupling between pions and nucleons,
$h_{\pi{NN}}^1$. The calculation performs measurements on dynamical anisotropic
clover gauge configurations, with a spatial extent of $L\sim2.5$ fm, a spatial
lattice 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 renormalization
of the bare parity-violating operators, a chiral extrapolation to the physical
pion mass, or contributions from disconnected (quark-loop) diagrams, these are
expected to result in systematic errors within the quoted statistical error. We
find 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-dependent
theoretical predictions.
