  We perform ab-initio calculations on Bi$_\mathrm{{Se}}$ antisite defects in
the surface of Bi$_2$Se$_3$, finding strong low-energy defect resonances with a
spontaneous ferromagnetism, fixed to an out-of-plane orientation due to an
exceptional large magnetic anisotropy energy. For antisite defects in the
surface layer, we find semi-itinerant ferromagnetism and strong hybridization
with the Dirac surface state, generating a finite energy gap. For deeper lying
defects, such hybridization is largely absent, the magnetic moments becomes
more localized, and no energy gap is present.
