Much like a neutral atom, a pair of electron and positron, bound by their mutual electric force, can travel freely across strong magnetic fields with unprecedented stability. Each of the electron and positron gyrates around its own guiding center in such a stable way that their classical orbits look like a pair of helices with the same helicity. Of particular interest is that when excited, a collection of these quasi-atoms with non-relativistic thermal velocities can produce broad-band emissions with a bandwidth covering a sizable fraction of the cyclotron frequency. A possible experimental setup for testing the existence of this peculiar positronium is suggested.