In very intense magnetic fields, B > 1.5 X 10(14) T, the breaking of the strong interaction SU(2) X SU(2) symmetry arranges itself so that instead of the neutral sigma field acquiring a vacuum expectation value it is the charged pi field that does and the magnetic field is screened. Details are presented for a magnetic field generated by a current in a wire; we show that the magnetic field is screened out to a distance rho0 approximately I/f(pi)m(pi) from the wire.