A pilot investigation of dichotic listening of CV stimuli was undertaken using seven adults who stutter (AWS) and a comparison group of seven adults who do not stutter (AWNS). The aim of this research was to investigate whether AWS show a difference in the strength of the right ear advantage (REA) in both undirected and directed attention tasks when compared to AWNS. The undirected attention task involved manipulating the interaural intensity difference (IID) of the CV stimuli presented to each ear. The CV stimuli were presented with equal intensity for the directed attention task. The undirected attention results indicated that both AWS and AWNS have a REA for processing speech information, with a primary difference observed between groups in regard to the IID point at which a REA shifts to a LEA. This crossing-over point occurred earlier for AWS, indicating a stronger right hemisphere involvement for the processing of speech compared to AWNS. No differences were found between groups in the directed attention task. The differences and similarities observed in dichotic listening between the two groups are discussed in regard to hemispheric specialization in the processing of speech.