Numerical simulations of the bosonic sector of the SU(2)× U(1) electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the W^± boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.