Antihydrogen has recently been produced in collisions of antiprotons with ions. While passing through the Coulomb field of a nucleus an antiproton will create an electron-positron pair. In rare cases the positron is bound by the antiproton and an antihydrogen atom produced. We calculate the production of relativistic antihydrogen atoms by bound-free pair production. The cross section is calculated in the semiclassical approximation (SCA), or equivalently in the plane wave Born approximation (PWBA) using exact Dirac-Coulomb wave functions. We compare our calculations to the equivalent photon approximation (EPA).