In this video economist Michael Kumhof shows that full reserve banking is not only possible but it actually work in a modern capitalist economy and that it is more stable than the current fractional reserve banking system.
The important point of the Chicago plan is that government and not private banks should control the money supply by issuing debt-free money. In order the do so, fractional reserve banking should be prohibited.
The paper referred to in the video can be found here.
For a more elementary introduction to modern banking, we refer to the videos by Richard Werner.