  Static and dynamical properties of weakly coupled antiferromagnetic spin
chains are treated using a mean--field approximation for the interchain
coupling and exact results for the resulting effective one--dimensional
problem. Results for staggered magnetization, N\'eel temperature and spin wave
excitations are in agreement with experiments on $\rm KCuF_3$. The existence of
a narrow longitudinal mode is predicted. The results are in agreement with
general scaling arguments, contrary to spin wave theory.
