OBJECTIVE: The efficacy of spoken language comprehension therapies for persons with aphasia remains equivocal. We investigated the efficacy of a self-led therapy app, 'Listen-In', and examined the relation between brain structure and therapy response. METHODS: A cross-over randomised repeated measures trial with five testing time points (12-week intervals), conducted at the university or participants' homes, captured baseline (T1), therapy (T2-T4) and maintenance (T5) effects. Participants with chronic poststroke aphasia and spoken language comprehension impairments completed consecutive Listen-In and standard care blocks (both 12 weeks with order randomised). Repeated measures analyses of variance compared change in spoken language comprehension on two co-primary outcomes over therapy versus standard care. Three structural MRI scans (T2-T4) for each participant (subgroup, n=25) were analysed using cross-sectional and longitudinal voxel-based morphometry. RESULTS: Thirty-five participants completed, on average, 85 hours (IQR=70-100) of Listen-In (therapy first, n=18). The first study-specific co-primary outcome (Auditory Comprehension Test (ACT)) showed large and significant improvements for trained spoken words over therapy versus standard care (11%, Cohen's d=1.12). Gains were largely maintained at 12 and 24 weeks. There were no therapy effects on the second standardised co-primary outcome (Comprehensive Aphasia Test: Spoken Words and Sentences). Change on ACT trained words was associated with volume of pretherapy right hemisphere white matter and post-therapy grey matter tissue density changes in bilateral temporal lobes. CONCLUSIONS: Individuals with chronic aphasia can improve their spoken word comprehension many years after stroke. Results contribute to hemispheric debates implicating the right hemisphere in therapy-driven language recovery. Listen-In will soon be available on GooglePlay. TRIAL REGISTRATION NUMBER: NCT02540889.