We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A2 for a kaon to decay into two π mesons with isospin 2. We find ReA2=(1.436±0.063stat±0.258syst)10-8 GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find ImA2=-(6.83±0.51stat±1.30syst)10-13 GeV. Moreover combining our result for ImA2 with experimental values of ReA2, ReA0, and ϵ'/ϵ, we obtain the following value for the unknown ratio ImA0/ReA0 within the standard model: ImA0/ReA0=-1.63(19)stat(20)syst×10-4. One consequence of these results is that the contribution from ImA2 to the direct CP violation parameter ϵ' (the so-called Electroweak Penguin contribution) is Re(ϵ'/ϵ)EWP=-(6.52±0.49stat±1.24syst)×10-4. We explain why this calculation of A2 represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP violation in kaon decays.