We present the first systematic spectropolarimetric study of Luminous Blue Variables (LBVs), and find that at least half those objects studied display evidence for intrinsic polarization -- a signature of significant inhomogeneity at the base of the wind. Furthermore, multi-epoch observations reveal that the polarization is variable in both strength and position angle. This evidence points away from a simple axi-symmetric wind structure `{a} la the B[e] supergiants, and instead suggests a wind consisting of localised density enhancements, or `clumps. We show with an analytical model that, in order to produce the observed variability, the clumps must be large, produced at or below the photosphere, and ejected on timescales of days. More details of LBV wind-clumping will be determined through further analysis of the model and a polarimetric monitoring campaign.
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