We present the first fully self-consistent three dimensional model of a neutron star's magnetic field, generated by electric currents in the star's crust via the Hall effect. We find that the global-scale field converges to a dipolar Hall-attractor state, as seen in recent axisymmetric models, but that small-scale features in the magnetic field survive even on much longer time scales. These small-scale features propagate toward the dipole equator, where the crustal electric currents organize themselves into a strong equatorial jet. By calculating the distribution of magnetic stresses in the crust, we predict that neutron stars with fields stronger than 10^{14} G can still be subject to starquakes more than 10^{5} yr after their formation.