  The "glassy" superconducting transition at high magnetic fields can be
induced by columnar disorder. A model is proposed in which the thermodynamics
of Bose condensation of Cooper pairs into the lowest Landau-level eigenstate of
the random potential can be solved exactly. The solution reflects a peculiar
character of the high-field limit: for example, the effective dimensionality of
the transition is shown to be a function of the magnetic field.
