  The longitudinal spin structure factor for the XXZ-chain at small wave-vector
q is obtained using Bethe Ansatz, field theory methods and the Density Matrix
Renormalization Group. It consists of a peak with peculiar, non-Lorentzian
shape and a high-frequency tail. We show that the width of the peak is
proportional to q^2 for finite magnetic field compared to q^3 for zero field.
For the tail we derive an analytic formula without any adjustable parameters
and demonstrate that the integrability of the model directly affects the
lineshape.
