  We study self avoiding random walks in an environment where sites are
excluded randomly, in two and three dimensions. For a single polymer chain, we
study the statistics of the time averaged monomer density and show that these
are well described by multifractal statistics. This is true even far from the
percolation transition of the disordered medium. We investigate solutions of
chains in a disordered environment and show that the statistics cease to be
multifractal beyond the screening length of the solution.
