  We investigate the wave dynamics of a charged massive scalar field
propagating in a maximally rotating (extremal) linear dilaton black hole
geometry. We prove the existence of a discrete and infinite family of
resonances describing non-decaying stationary scalar configurations (clouds)
enclosing these rapidly rotating black holes. The results obtained signal the
potential stationary scalar field distributions (dark matter) around the
extremal linear dilaton black holes. In particular, we analytically compute the
effective heights of those clouds above the center of the black hole.
