  Dirac-like surface states on surfaces of topological insulators have a chiral
spin structure that suppresses back-scattering and protects the coherence of
these states in the presence of non-magnetic scatterers. In contrast, magnetic
scatterers should open the back- scattering channel via the spin-flip processes
and degrade the state's coherence. We present angle-resolved photoemission
spectroscopy studies of the electronic structure and the scattering rates upon
adsorption of various magnetic and non-magnetic impurities on the surface of
Bi$_2$Se$_3$, a model topological insulator. We reveal a remarkable
insensitivity of the topological surface state to both non-magnetic and
magnetic impurities in the low impurity concentration regime. Scattering
channels open up with the emergence of hexagonal warping in the high-doping
regime, irrespective of the impurity's magnetic moment.
