The ipsilesional arm of stroke patients often has functionally limiting deficits in motor control and dexterity that depend on the side of the brain that is lesioned and that increase with the severity of paretic arm impairment. However, remediation of the ipsilesional arm has yet to be integrated into the usual standard of care for upper limb rehabilitation in stroke, largely due to a lack of translational research examining the effects of ipsilesional-arm intervention. We now ask whether ipsilesional-arm training, tailored to the hemisphere-specific nature of ipsilesional-arm motor deficits in participants with moderate to severe contralesional paresis, improves ipsilesional arm performance and generalizes to improve functional independence. We assessed the effects of this intervention on ipsilesional arm unilateral performance [Jebsen–Taylor Hand Function Test (JHFT)], ipsilesional grip strength, contralesional arm impairment level [Fugl–Meyer Assessment (FM)], and functional independence [Functional independence measure (FIM)] (N = 13). Intervention occurred over a 3 week period for 1.5 h/session, three times each week. All sessions included virtual reality tasks that targeted the specific motor control deficits associated with either left or right hemisphere damage, followed by graded dexterity training in real-world tasks. We also exposed participants to 3 weeks of sham training to control for the non-specific effects of therapy visits and interactions. We conducted five test-sessions: two pre-tests and three post-tests. Our results indicate substantial improvements in the less-impaired arm performance, without detriment to the paretic arm that transferred to improved functional independence in all three posttests, indicating durability of training effects for at least 3 weeks. We provide evidence for establishing the basis of a rehabilitation approach that includes evaluation and remediation of the ipsilesional arm in moderately to severely impaired stroke survivors. This study was originally a crossover design; however, we were unable to complete the second arm of the study due to the COVID-19 pandemic. We report the results from the first arm of the planned design as a longitudinal study.