Summary: This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [S. Jitman and P. Udomkavanich, Int. J. Contemp. Math. Sci. 5, No. 9–12, 449–458 (2010; Zbl 1191.94121)] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by M. Shi et al. in [J. Franklin Inst. 350, No. 5, 929–937 (2013; Zbl 1293.94114)].