Ly alpha nebulae, or "Ly alpha blobs," are extended (up to similar to 100 kpc), bright (L-Ly alpha greater than or similar to 10(43) erg s(-1)) clouds of Lya emitting gas that tend to lie in overdense regions at z similar to 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 blob's Lya emission peak, and its radio lobes align roughly with the blob's major axis. With the SPOL polarimeter on the 6.5 m MMT telescope, we map the total (Ly alpha + continuum) polarization in a grid of circular apertures of a radius of 0.'' 6 (4.4 kpc), detecting a significant (>2 sigma) polarization fraction P-% in nine apertures and achieving strong upper limits (as low as 2%) elsewhere. P-% increases from <2% at similar to 5 kpc from the blob center to 17% at similar to 15-25 kpc. The detections are distributed asymmetrically, roughly along the nebula's major axis. The polarization angles theta are mostly perpendicular to this axis. Comparing the Ly alpha 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-%,P-Ly alpha ranging from no significant polarization at similar to 5 kpc from the blob center to 3%-17% at 10-25 kpc. Like the total polarization, the Ly alpha polarization detections occur more often along the blob's major axis.