Phonons are known to generate a thermal Hall effect in certain insulators, including oxides with rare-earth impurities, quantum paraelectrics, multiferroic materials, and cuprate Mott insulators. In each case, a special feature of the material is presumed relevant for the underlying mechanism that confers chirality to phonons in a magnetic field. A fundamental question is whether a phonon Hall effect is an unusual occurrence—linked to special characteristics such as skew scattering off rare-earth impurities, structural domains, ferroelectricity, or ferromagnetism—or a much more common property of insulators than hitherto believed. To help answer this question, we have turned to a material with none of the previously encountered special features: the cubic antiferromagnet Cu₃TeO₆. We find that its thermal Hall conductivityκxyis among the largest of any insulator so far. We show that this record-highκxysignal is due to phonons, and it does not require the presence of magnetic order, as it persists above the ordering temperature. We conclude that the phonon Hall effect is likely to be a fairly common property of solids.