In cochlear implant (CI) recipients with unilateral hearing loss (UHL) and normal hearing (NH) in the contralateral ear, the central auditory system receives signals of different auditory modalities, i.e. electrically via the CI ear as well as acoustically via the NH ear. The present study investigates binaural integration of bimodal stimulation in the central auditory system of 10 CI subjects with UHL by applying a modified version of the Rapidly Alternating Speech Perception (RASP) test to characterise speech recognition ability under monotic and dichotic listening arrangements. Subsequently, the results for each monotic and dichotic test condition were compared to quantify the binaural benefit from CI usage. The study results demonstrate significantly improved speech recognition under dichotic compared to monotic listening conditions, providing evidence that there is binaural integration of acoustically and electrically transmitted speech segments in the central nervous system at brainstem and cortical levels. In contrast to more commonly used tests of binaural integration, such as localisation, the RASP test provides the clinical option to investigate binaural integration involving structures at the cortical level.