The gapless surface states of strong topological insulators have drawn a great deal of attention over the past few years.

In a previous work  it was shown that for a strong enough electron-electron interaction the surface of a strong topological insulator is unstable to the formation

of spontaneous uniform magnetization.

In this work we analyzed the instability conditions for spin-density-waves (SDW) formation on the surface of strong topological insulators. We find that for a

certain range of energies the SDW instability is favored compared to the uniform one. We also find that the SDW are of spiral nature and for a certain range of

parameters a Skyrmion-lattice is formed on the surface. We show that this phase may have a non trivial Chern-number even in the absence of an external magnetic

field. Finally, we claim that a controlled network of one-dimensional chiral channels can be established on the surface of a strong topological insulator.