Transfers a sulfate group to the hydroxyl group at C3 of non-reducing beta-galactosyl residues. Acts both on type 1 (Gal-beta-1,3-GlcNAc) and type 2 (Gal-beta-1,4-GlcNAc) chains with similar efficiency. Strongly inhibited by Cu(2+) and Zn(2+). Optimum pH is 6.0-6.5. Protein modification; carbohydrate sulfation. Ubiquitous. Detected in heart, stomach, colon, liver and spleen, in epithelial cells lining the lower to middle layer of the crypts in colonic mucosa, hepatocytes surrounding the central vein of the liver, extravillous cytotrophoblasts in the basal plate of the septum of the placenta, renal tubules of the kidney, and neuronal cells of the cerebral cortex. Belongs to the galactose-3-O-sulfotransferase family.