We report the first observation of electron momentum contributions to the Doppler broadening of radiation produced by in-flight two-photon annihilation in solids. In these experiments an approximately 2.5 MeV positron beam impinged on thin polyethylene, aluminum, and gold targets. Since energetic positrons easily penetrate the nuclear Coulomb potential and do not cause a strong charge polarization, the experimental annihilation line shapes agree well with calculations based on a simple independent-particle model. Moreover, annihilations with the deepest core electrons are greatly enhanced.