We show that K2ZnSn3S8 is a phase-change system that exhibits tristability. Kinetic and thermodynamic forms of different compounds in the K/Zn/Sn/S system have been synthesized and thoroughly characterized. We report an example where slow and rapid cooling of a melt of K2CO3/S/Sn/Zn leads to different kinetically stable products (crystalline layered alpha-K2ZnSn3S8, 1, and glassy K2ZnSn3S8, A, respectively). These forms convert to a thermodynamically stable compound (crystalline cubic beta-K2ZnSn3S8, 2) upon annealing below their melting points. The band gaps of compounds 1, A, and 2 are 2.30, 2.15, and 2.55 eV, respectively.