We study the  XXZ quantum spin chain in  a random field. This model is particle number preserving, which allows  the reduction to an infinite system of discrete many-body random Schrodinger operators.  We exploit this reduction to prove a form of  Anderson localization in the droplet  spectrum of the XXZ quantum spin chain Hamiltonian. This yields a strong form of dynamical exponential clustering for eigenstates  in the droplet spectrum: For any pair of local observables,  the sum of the associated correlators over these states decays exponentially  in the distance between the  local observables. Moreover,  this exponential clustering persists under the time evolution in the  droplet spectrum.