Listening in a noisy environment is challenging for individuals with normal hearing and can be a significant burden for those with hearing impairment. The extent to which this burden is alleviated by a hearing device is a major, unresolved issue for rehabilitation. Here, we found adult users of cochlear implants (CIs) self-reported listening effort during a speech-in-noise task that was positively related to alpha oscillatory activity in the left inferior frontal cortex, canonical Broca's area, and inversely related to speech envelope coherence in the 2-5 Hz range originating in the superior-temporal plane encompassing auditory cortex. Left frontal cortex coherence in the 2-5 Hz range also predicted speech-in-noise identification. These data demonstrate that neural oscillations predict both speech perception ability in noise and listening effort.