Suggesting a novel sample design (impurities in the middle of the barrier separating two quantum wells), we propose a method to investigate the Coulomb drag effect in double layers with correlated disorder. We predict that for strongly correlated impurity potentials the low-temperature drag will be substantially enhanced as compared to the conventional (uncorrelated) situation, due to a possibility of a coherent diffusive motion of carriers propagating in different layers. The influence of magnetic field and interlayer tunneling is also discussed.