Having both the positron and electron beams polarized in a future linear e + e − collider is a decisive improvement for many physics studies at such a machine. The motivation for polarized positrons, and a demonstration experiment for the undulator-based production of polarized positrons are reviewed. This experiment ('E-166') uses the 50 GeV Final Focus Test electron beam at SLAC with a 1 m-long helical undulator to make ≈ 10M eV polarized photons. These photons are then converted in a thin (≈ 0.5 radiation length) target into positrons (and electrons) with about 50% polarization. FOR THE E-166 COLLABORATION * Having both the positron and electron beams polarized in a future linear e + e − collider is a decisive improvement for many physics studies at such a machine. The motivation for polarized positrons, and a demonstration experiment for the undulator-based production of polarized positrons are reviewed. This experiment ('E-166') uses the 50 GeV Final Focus Test electron beam at SLAC with a 1 m-long helical undulator to make ≈ 10MeV polarized photons. These photons are then converted in a thin (≈ 0.5 radiation length) target into positrons (and electrons) with about 50% polarization.