  We identify a new superintegrable Hamiltonian in 3 degrees of freedom,
obtained as a reduction of pure Keplerian motion in 6 dimensions. The new
Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r
potential with three barrier terms preventing the particle crossing the
principal planes. In 3 degrees of freedom, there are 5 functionally independent
integrals of motion, and all bound, classical trajectories are closed and
strictly periodic. The generalisation of the Laplace-Runge-Lenz vector is
identified and shown to provide functionally independent isolating integrals.
They are quartic in the momenta and do not arise from separability of the
Hamilton-Jacobi equation. A formulation of the system in action-angle variables
is presented.
