Cochlear implant (CI) users frequently achieve good speech understanding based on phoneme and word recognition. However, there is a significant variability between CI users in processing prosody. The aim of this study was to examine the abilities of an excellent CI user to segment continuous speech using intonational cues. A post-lingually deafened adult CI user and 22 normal hearing (NH) subjects segmented phonemically identical and prosodically different sequences in French such as 'l'affiche' (the poster) versus 'la fiche' (the sheet), both [lafiʃ]. All participants also completed a minimal pair discrimination task. Stimuli were presented in auditory-only and audiovisual presentation modalities. The performance of the CI user in the minimal pair discrimination task was 97% in the auditory-only and 100% in the audiovisual condition. In the segmentation task, contrary to the NH participants, the performance of the CI user did not differ from the chance level. Visual speech did not improve word segmentation. This result suggests that word segmentation based on intonational cues is challenging when using CIs even when phoneme/word recognition is very well rehabilitated. This finding points to the importance of the assessment of CI users' skills in prosody processing and the need for specific interventions focusing on this aspect of speech communication.