  We report on an experimental realization of unidirectional transporting
island structures in an otherwise chaotic phase space of the delta-kicked rotor
system. Using a Bose-Einstein Condensate as a source of ultracold atoms, we
employ asymmetric phase modulation in the kicks, with the narrow momentum
distribution of the atoms allowing us to address individual island structures.
We observe quantum ratchet behavior in this system, with clear directed
momentum current in the absence of a directional force, which we characterize
and connect to \epsilon-classical theory.
