  We examine Chern-Simons theory written on a noncommutative plane with a
`hole', and show that the algebra of observables is a nonlinear deformation of
the $w_\infty$ algebra. The deformation depends on the level (the coefficient
in the Chern-Simons action), and the noncommutativity parameter, which were
identified, respectively, with the inverse filling fraction and the inverse
density in a recent description of the fractional quantum Hall effect. We
remark on the quantization of our algebra. The results are sensitive to the
choice of ordering in the Gauss law.
