Neuroelectric imaging methods (electroencephalography and magnetoencephalography) can reveal cortical activity phase locked to amplitude modulation in sensory inputs for frequencies up to about 100 Hz. The neural response at the input modulation frequency is known as the visual or auditory steady-state responses (VSSR or ASSR, depending on input modality). In vision, VSSR strength is modulated by attention: energy in the frequency modulating an attended object is enhanced, while the VSSR to a distracting object is suppressed. However, in the literature, attention causes less consistent effects on the auditory steady-state response. We combined M/EEG to study how the ASSR is modulated when listeners focus spatial attention on one of two speech streams. We find that attention enhances the ASSR power at the frequency of an attended stream in auditory cortex contralateral to the attended direction. The attended-stream modulation frequency also drives phase-locked responses in left, but not right precentral sulcus (which is associated with control eye gaze and spatial attention). This asymmetric activation of the attentional network helps explain seemingly contradictory results of past auditory studies, most of which used dichotic rather than binaural simuli and analyzed results in sensor space or assumed particular dipole solutions rather than doing whole-brain analysis.