A theoretical prediction of a new spin effect by Tamura, Piepke, and Feder has been experimentally verified: Photoelectrons can be polarized even if the photoemission is performed with linearly polarized radiation and even if it is studied in the highly symmetrical setup of normal incidence and normal emission. Radiation with energies between 21 and 22.4 eV ejects photoelectrons from Pt(111) polarized with a degree between 10% and 40%. The spin direction coincides with a plane parallel to the surface and changes its sign when the crystal is rotated by 60° about the surface normal.