  Quantum Mechanics in the non-commutative plane is shown to admit the
``exotic'' symmetry of the doubly-centrally-extended Galilei group. When
coupled to a planar magnetic field whose strength is the inverse of the
non-commutative parameter, the system becomes singular, and ``Faddeev-Jackiw''
reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and
Trugenberger. The reduced system moves according to the Hall law.
