Recently, the LHCb Collaboration discovered the first doubly charmed baryon Ξcc++=ccu at 3621.40±0.78 MeV, very close to our theoretical prediction. We use the same methods to predict a doubly bottom tetraquark T(bbūd-) with JP=1+ at 10 389±12 MeV, 215 MeV below the B-B-∗0 threshold and 170 MeV below the threshold for decay to B-B-0γ. The T(bbūd-) is therefore stable under strong and electromagnetic interactions and can only decay weakly, the first exotic hadron with such a property. On the other hand, the mass of T(ccūd-) with JP=1+ is predicted to be 3882±12 MeV, 7 MeV above the D0D∗+ threshold and 148 MeV above the D0D+γ threshold. T(bcūd-) with JP=0+ is predicted at 7134±13 MeV, 11 MeV below the B-0D0 threshold. Our precision is not sufficient to determine whether bcūd- is actually above or below the threshold. It could manifest itself as a narrow resonance just at threshold.