In dichotic listening, subjects are apparently unable to attend simultaneously to two concurrent, auditory speech messages. However, in two experiments reported here, it is shown that people can attend to and repeat back continuous speech at the same time as taking in complex, unrelated visual scenes, or even while sightreading piano music. In both cases performance with divided attention was very good, and in the case of sight-reading was as good as with undivided attention. There was little or no effect of the dual task on the accuracy of speech shadowing. These results are incompatible with the hypothesis that human attention is limited by the capacity of a general-purpose central processor in the nervous system. An alternative, "multi-channel", hypothesis is outlined.