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We report the first measurements of the polarization of x rays emitted from bound-bound transitions in a highly ionized He-like ion. Polarization was measured for the decay to the ground state, 1{ital s}{sup 2} {ital S}{sub 0}, of the He-like Sc{sup 19+} levels 1{ital s}2{ital p} {sup 1}{ital P}{sub 1}, 1{ital s}2{ital p} {sup 3}{ital P}{sub 2}, 1{ital s}2{ital p} {sup 3}{ital P}{sub 1}, and 1{ital s}2{ital s} {sup 3}{ital S}{sub 1}. The measurements were made with the Electron Beam Ion Trap at two electron-beam energies: 4.36 and 5.62 keV. Polarization of two of the lines is strongly influenced by the hyperfine interaction with the Sc nucleus, demonstrating that polarization measurements can be used to investigate hyperfine interactions in highly ionized atoms.