We report the first lattice QCD calculation of the complex kaon decay amplitude with physical kinematics, using a lattice volume and a single lattice spacing , with . We find and Im(A0)=-1.90(1.23)(1.08)×10-11  GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: , while the second can be used to compute the direct -violating ratio , which is below the experimental value . The real part of is conserving and serves as a test of our method while the result for provides a new test of the standard model theory of violation, one which can be made more accurate with increasing computer capability.