AgCu nanoalloys are known to exhibit a size dependent transition to the chiral stacking from the anti-Mackay stacking. In the current work, the role of composition on the structural transitions between the anti-Mackay and the chiral stacking in AgCu nanoalloys has been studied computationally using a combination of global optimization searches and heating simulations. It is observed that in addition to the size, composition also affects the surface stacking in these nanoalloys. Further, results show that the nature of the recently reported thermally induced transition to the chiral stacking is strongly dependent on the Cu content in the AgCu nanoalloys. The amount of Cu in the nanoalloy affects both the transition temperature and the “sharpness” of the transition. By analyzing the frequencies of the vibrational modes calculated using the Harmonic Superposition Approximation (HSA), the thermal stability of the chiral stacking is attributed to the vibrational entropic contribution. Finally, the findings in the current work have been consolidated in the form of a size-composition map. By referring to this size-composition map, the preference for the chiral stacking can be understood for the nanoalloys belonging to the size window between the “magic” sized nanoalloys. © 2020 Elsevier B.V.