  Euler's three-body problem is the problem of solving for the motion of a
particle moving in a Newtonian potential generated by two point sources fixed
in space. This system is integrable in the Liouville sense. We consider the
Euler problem with the inverse-square potential, which can be seen as a natural
generalization of the three-body problem to higher-dimensional Newtonian
theory. We identify a family of stable stationary orbits in the generalized
Euler problem. These orbits guarantee the existence of stable bound orbits.
Applying the Poincar\'e map method to these orbits, we show that stable bound
chaotic orbits appear. As a result, we conclude that the generalized Euler
problem is nonintegrable.
