As is known, so far only helium has appeared to be unique quantum liquid which does not solidify and becomes supeffluid at low temperature. The situation is dramatically changed in presence of a strong magnetic field such that the distance between the Landau levels exceeds the Coulomb unit of energy. Under the circumstances, the interaction between hydrogenlike atoms in the triplet ground state is strongly anisotropic and pretty weak. For such a Bose gas of hydrogenlike atoms, there is a possibility of forming a Bose condensate and a superfluid state. The importance of the problem is due to the fact that it arises in various areas of physics, especially in astrophysics and physics of semiconductors. In semiconductors, a high density exciton gas is the unique object for the laboratory studies of the extreme states of matter in a ultrastrong magnetic field, where the "atomic" scale of a magnetic field for the hydrogenlike excitons is of the order of a few Tesla, quite realizable in a laboratory.