Recently, the LHCb Collaboration discovered the first doubly charmed baryon Ξ_{cc}^{++}=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(bbu[over ¯]d[over ¯]) with J^{P}=1^{+} at 10 389±12 MeV, 215 MeV below the B^{-}B[over ¯]^{*0} threshold and 170 MeV below the threshold for decay to B^{-}B[over ¯]^{0}γ. The T(bbu[over ¯]d[over ¯]) 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(ccu[over ¯]d[over ¯]) with J^{P}=1^{+} is predicted to be 3882±12 MeV, 7 MeV above the D^{0}D^{*+} threshold and 148 MeV above the D^{0}D^{+}γ threshold. T(bcu[over ¯]d[over ¯]) with J^{P}=0^{+} is predicted at 7134±13 MeV, 11 MeV below the B[over ¯]^{0}D^{0} threshold. Our precision is not sufficient to determine whether bcu[over ¯]d[over ¯] is actually above or below the threshold. It could manifest itself as a narrow resonance just at threshold.