We discuss our recent publication (arXiv:1505.07863 [hep-lat]) of the first lattice QCD calculation of the complex kaon decay amplitude A_0 with physical kinematics, using a single 32^3 x 64 domain wall ensemble with G-parity spatial boundary conditions. We obtain approximate agreement with the experimental value for Re(A_0), which serves as a test of our method. Our prediction of Im(A_0) can be used to compute the direct CP violating ratio Re(ε′/ε), which we find to be ~2 sigma lower than the experimental value. This result provides a new test of the Standard Model theory of CP violation, one which can be made more accurate with increasing computer capability.