Structure and quantum effects of a Cl 2 molecule embedded in fcc and hcp para-hydrogen (pH 2 ) crystals are investigated in the zero-temperature limit. The interaction is modelled in terms of Cl 2 -pH 2 and pH 2 -pH 2 pair potentials from ab initio CCSD(T) and MP2 calculations. Translational and rotational motions of the molecules are described within three-dimensional anharmonic Einstein and Devonshire models, respectively, where the crystals are either treated as rigid or allowed to relax. The pH 2 molecules, as well as the heavier Cl 2 molecule, show large translational zero-point energies (ZPEs) and undergo large-amplitude translational motions. This gives rise to substantial reductions in the cohesive energies and expansions of the lattices, in agreement with experimental results for pure hydrogen crystals. The rotational dynamics of the Cl 2 impurity is restricted to small-amplitude librations, again with high librational ZPEs, which are described in terms of two-dimensional non-degenerate anharmonic oscillators. The lattice relaxation causes qualitative changes of the rotational energy surfaces, which finally favour librations around the crystallographic directions pointing towards the nearest neighbours, both for fcc and hcp lattices. Implications on the reactant orientation in the experimentally observed laser-induced chemical reaction, Cl + H 2 → HCl + H, are discussed.