SLAC E-158 is an experiment designed to make the first measurement of parity violation in Møller scattering. E-158 will measure the right-left cross-section asymmetry, A M øller LR , in the elastic scattering of a 45-GeV polarized electron beam off unpolarized electrons in a liquid hydrogen target. E-158 plans to measure the expected Standard Model asymmetry of ∼ 10 −7 to an accuracy of better than 10 −8 . To make this measurement, the polarized electron source requires for operation an intense circularly polarized laser beam and the ability to quickly switch between right-and left-helicity polarization states with minimal right-left helicity-correlated asymmetries in the resulting beam parameters (intensity, position, angle, spot size, and energy), beam A LR 's. This laser beam is produced by a unique SLAC-designed flashlamp-pumped Ti:Sapphire laser and is propagated through a carefully designed set of polarization optics. We analyze the transport of nearly circularly polarized light through the optical system and identify several mechanisms that generate beam A LR 's. We show that the dominant effects depend linearly on particular polarization phase shifts in the optical system. We present the laser system design and a discussion of the suppression and control of beam A LR 's. We also present results on beam performance from engineering and physics runs for E-158.