  A method for deriving superintegrable Hamiltonians with a spin orbital
interaction is presented. The method is applied to obtain a new superintegrable
system in Euclidean space $\mathbb{E}_3$ with the following properties. It
describes a rotationally invariant interaction between a particle of spin
$\frac{1}{2}$ and one of spin 0. Its Hamiltonian commutes with total angular
momentum $\vec{\mathcal{J}}$ and with additional vector integrals of motion
$\vec{X}$, $\vec{Y}$ with components that are third order differential
operators. The integrals of motion form a polynomial algebra under commutation.
The system is exactly solvable (in terms of Laguerre polynomials) and the bound
state energy levels are degenerate and described by a Balmer type formula. When
the spin orbital potential is switched off the system reduces to a hydrogen
atom.
