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We consider the polarization of 21cm line radiation from the epoch ofreionization due to both intrinsically polarized emission and secondarymechanisms. We argue that Thomson scattering of the 21cm quadrupole by thereionized universe is likely to produce the largest effect. The 21cm quadrupoleis sourced by baryonic density fluctuations and the fluctuations in theionization fraction due to discrete \ion{H}{2} regions. Since Thomsonscattering produces only E-type polarization and is achromatic, its uniquefingerprint can in principle be separated from foregrounds associated withpolarized synchrotron emission which should not be correlated with the cosmicsignal. We estimate that Poisson fluctuations of \ion{H}{2} regions at the endof reionization ($z_R \sim 6$--20) produce a brightnesstemperature-polarization cross-correlation signal of $\sim 0.1 - 0.3 {mK}$ onangular scales of tens of arcminutes. This cross-correlation signal is withinthe instrument sensitivities of the future {\it Square Kilometer Array} (SKA)and close to the sensitivities of the forthcoming {\it Mileura Widefield Array}(MWA) and {\it Low Frequency Array} (LOFAR).Comment: 10 pages, 6 figures, replaced to match version accepted by Ap

Polarization of 21 cm Radiation from the Epoch of Reionization