We report the first measurement of magnon thermal conductivity in monodomain single crystals of 3 He in the U2D2 antiferromagnetic phase. The magnon mean free path λ was found first to rise rapidly upon cooling below T N and then more slowly at low temperatures, depending upon the sample. The temperature dependence is consistent with magnon umklapp scattering at high T, i.e., λ proportional to T −2 exp(Δ/k B T), with Δ/k B determined to be 5.8(±0.3) mK. The limiting low-temperature values of λ varied from 0.3 to 3 μm