  The Heisenberg XXZ spin-1/2 chain is considered in the massive
antiferromagnetic regime in the presence of a staggered longitudinal magnetic
field. The Hamiltonian of the model is characterised by the anisotropy
parameter $\Delta<-1$, and by the magnetic field strength h. At zero magnetic
field, the model is exactly solvable. In the thermodynamic limit, it has two
degenerate vacua and the kinks (which are also called spinons) interpolating
between these vacua, as elementary excitations. Application of the staggered
magnetic field breaks integrability of the model and induces the long-range
attractive potential between two adjacent kinks leading to their confinement
into the bound states. The energy spectra of the resulting two-kink bound
states are perturbatively calculated in the extreme anisotropic (Ising) limit
$\Delta\to-\infty$ to the first order in the inverse anisotropy constant
$|\Delta|^{-1}$, and also for generic values of $\Delta<-1$ to the first order
in the weak magnetic field h.
