  We study the ground state and low-lying excitations of the S=1/2 XXZ
antiferromagnet on the kagome lattice at magnetization one third of the
saturation. An exponential number of non-magnetic states is found below a
magnetic gap. The non-magnetic excitations also have a gap above the ground
state, but it is much smaller than the magnetic gap. This ground state
corresponds to an ordered pattern with resonances in one third of the hexagons.
The spin-spin correlation function is short ranged, but there is long-range
order of valence-bond crystal type.
