If there is a large-scale anisotropy in the expansion of the Universe, the microwave background radiation is expected to be linearly polarized. This Communication shows that spatial curvature is capable of rotating the polarization of the microwaves relative to its direction at last scattering, which is directly correlated with the expansion anisotropy (and so also the observed intensity anisotropy). In Friedmann-Robertson-Walker models of the Universe with additional small expansion anisotropy, the observed rotation relative to the intensity anisotropy would be appreciable and constant over the celestial sphere in the closed (type IX) model, but in the flat and open models, it must either vanish (types I and V) or vary in a complicated way over the celestial sphere (type ${\mathrm{VII}}_h$). These facts suggest a clear observational test of the closure of the Universe. Also, an ambiguity inherent in the homogeneity of the Universe does not allow prediction of the direction of rotation; thus homogeneous universes possess a property which might be called "handedness."

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