The Chemla effect concerns the strong composition dependence of the internal ionic mobilities of cations in mixtures of two molten salts with a common anion, in which the mobility of the large cation can be higher than the small one at low concentrations of the latter. Molecular dynamics simulations of molten (Li,Cs)NO3, (Li,K)NO3, (Li,Na)NO3, (Na,Cs)NO3, each at two different compositions at a given temperature, and also pure LiNO3 and pure KNO3, have been performed with the aim of reproducing the Chemla effect. The key role played by anion polarization on the Chemla effect in molten alkali nitrates is demonstrated by comparing the calculated mobilities using nonpolarizable and polarizable models. Polarization effects were included in the simulations by using a previously proposed fluctuating charge model (FCM) for the NO3- anion. It is shown that a single potential model for a (M-1,M-2)NO3 mixture gives the correct composition dependence of the M-1 and the M-2 mobilities provided that polarization effects are included in the model. The FCM is thus transferable between different systems, but not its nonpolarizable counterpart. Structure and dynamics of the simulated systems are discussed in light of proposed models for the Chemla effect.