In the retina, directionally selective ganglion cells respond with robust spiking to movement in their preferred direction, but show minimal response to movement in the opposite, or null, direction. The mechanisms and circuitry underlying this computation have remained controversial. Here we show, by isolating the excitatory and inhibitory inputs to directionally selective cells and measuring direct connections between these cells and presynaptic neurons, that a presynaptic interneuron, the starburst amacrine cell, delivers direct inhibition to directionally selective cells. The processes of starburst cells are connected asymmetrically to directionally selective cells: those pointing in the null direction deliver inhibition; those pointing in the preferred direction do not. Starburst cells project inhibition laterally ahead of a stimulus moving in the null direction. In addition, starburst inhibition is itself directionally selective: it is stronger for movement in the null direction. Excitation in response to null direction movement is reduced by an inhibitory signal acting at a site that is presynaptic to the directionally selective cell. The interplay of these components generates reduced excitation and enhanced inhibition in the null direction, thereby ensuring robust directional selectivity.