The Continuous Electron Beam Accelerator Facility (CEBAF) was built with a thermionic electron source and the three original experimental hall lines reflected this. A few years after beam delivery began a parity violation experiment was approved and two polarimeters were installed in the Hall A beam line without consultation with the accelerator physics group. The beam raster system was placed after the new Compton polarimeter, before one accelerator quadrupole and four quadrupoles in the new Moller polarimeter. It was very difficult to meet experimental requirements on envelope functions and raster shape with this arrangement so a member of the accelerator physics group had a sixth quadrupole installed downstream of the Moller polarimeter. All of the parity experiments in Hall A have been run with this still-unsatisfactory configuration. The MOLLER experiment is predicated on achieving a 2% error on a 32 ppb asymmetry. Beam line changes are required to meet the systematic error budget. This paper documents the existing beam line, an interim change which can be accomplished during a annual maintenance down, and the final configuration for MOLLER and subsequent experiments.