Lya nebulae, or Lya blobs, are extended (up to ~100 kpc), bright (L[Lya] > 10^43 erg/s) clouds of Lya emitting gas that tend to lie in overdense regions at z ~ 2--5. The origin of the Lya emission remains unknown, but recent theoretical work suggests that measuring the polarization might discriminate among powering mechanisms. Here we present the first narrowband, imaging polarimetry of a radio-loud Lya nebula, B3 J2330+3927 at z=3.09, with an embedded active galactic nucleus (AGN). The AGN lies near the blobs Lya emission peak and its radio lobes align roughly with the blobs major axis. With the SPOL polarimeter on the 6.5m MMT telescope, we map the total (Lya + continuum) polarization in a grid of circular apertures of radius 0.6 (4.4kpc), detecting a significant (>2sigma) polarization fraction P in nine apertures and achieving strong upper-limits (as low as 2%) elsewhere. P increases from <2% at ~5kpc from the blob center to ~17% at ~15-25kpc. The detections are distributed asymmetrically, roughly along the nebulas major axis. The polarization angles theta are mostly perpendicular to this axis. Comparing the Lya flux to that of the continuum, and conservatively assuming that the continuum is highly polarized (20-100%) and aligned with the total polarization, we place lower limits on the polarization of the Lya emission P(Lya) ranging from no significant polarization at ~5 kpc from the blob center to ~ 3--17% at 10--25kpc. Like the total polarization, the Lya polarization detections occur more often along the blobs major axis.
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