Noise in the transduction of chemotactic stimuli to the flagellar motor of E. coli will affect the random run-and-tumble motion of the cell and the ability to perform chemotaxis. Here we use numerical simulations to show that an intermediate level of noise in the slow methylation dynamics enhances drift while not compromising localization near concentration peaks. A minimal model shows how such an optimal noise level arises from the interplay of noise and the dependence of the motor response on the network output. Our results suggest that cells can exploit noise to improve chemotactic performance.