The chain dynamics of unentangled polymers strongly deviates from the expected Rouse behavior when they form part of dynamically asymmetric polymer blends. These are miscible systems where the two components display very different segmental mobility (or glass transition). The generalized Langevin equation formalism seems to be a suitable theoretical framework for this situation. In this Work we have used an approximation based on (i) a simplified generalized Langevin equation and (ii) the phenomenological result of nonexponential decay of the Rouse model correlators in asymmetric polymer blends. In the framework of this approximation, we have deduced an incoherent scattering function for chain dynamics of unentangled polymers in asymmetric blends. This function-which in the Rouse limit reduces to the well-known de Gennes expression-is validated by molecular dynamics simulation results of a canonical asymmetric blend: poly(methyl methacrylate)/poly(ethylene oxide).