  Peaking consistently in June for nearly eleven years, the annual modulation
signal reported by DAMA/NaI and DAMA/LIBRA offers strong evidence for the
identity of dark matter. DAMA's signal strongly suggest that dark matter
inelastically scatters into an excited state split by O(100 keV). We propose
that DAMA is observing hyperfine transitions of a composite dark matter
particle. As an example, we consider a meson of a QCD-like sector, built out of
constituent fermions whose spin-spin interactions break the degeneracy of the
ground state. An axially coupled U(1) gauge boson that mixes kinetically with
hypercharge induces inelastic hyperfine transitions of the meson dark matter
that can explain the DAMA signal.
