To determine the direction of a sound source in space, animals must process a variety of auditory spatial cues, including interaural level and time differences, as well as changes in the sound spectrum caused by the direction-dependent filtering of sound by the outer ear. Behavioural deficits observed when primary auditory cortex (A1) is damaged have led to the widespread view that A1 may have an essential role in this complex computational task. Here we show, however, that the spatial selectivity exhibited by the large majority of A1 neurons is well predicted by a simple linear model, which assumes that neurons additively integrate sound levels in each frequency band and ear. The success of this linear model is surprising, given that computing sound source direction is a necessarily nonlinear operation. However, because linear operations preserve information, our results are consistent with the hypothesis that A1 may also form a gateway to higher, more specialized cortical areas.