We present the first lattice QCD calculation of the leading-order momentum-independent parity violating coupling between pions and nucleons, h 1 πNN . The calculation performs measurements on dynamical anisotropic clover gauge configurations, with a spatial extent of L ∼ 2.5 fm, a spatial lattice spacing of as ∼ 0.123 fm, and a pion mass of mπ ∼ 389 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 1,con πNN = (1.099 ± 0.505 +0.058 −0.064 ) × 10 −7 , consistent with current experimental bounds and previous model-dependent theoretical predictions.