Currently there is a great amount of scientific research directed at ratchet devices and mechanisms. Initially stimulated by a need to understand biological systems, the field has widened to encompass mesoscopic and atomic physics as well as quantum effects. The great majority of this effort has been directed at systems which include noise (Brownian ratchets). Comparatively little work has been undertaken on deterministic ratchets (i.e. with no noise but possibly including dissipation). Prior to our work there had only been two studies of Hamiltonian ratchets (no noise or dissipation) which concluded that only mixed-phase space mechanisms were feasible. However, the work in this thesis proposes a new fully chaotic, noise-free, Hamiltonian ratchet. This ratchet system is studied in both the quantum and classical regimes and is found to produce, reversible, non-zero currents for well chosen parameter values. The ratchet mechanism proposed in this thesis is has now been implemented experimentally with ultra-cold cesium atoms in a pulsed optical lattice. Optimum system parameters are suggested to produce the best experimental signature for the ratchet. The work presented here has inspired further experimental work for the specific Hamiltonian of the system.