Chronic stroke survivors with severe contralesional arm paresis face numerous challenges to performing activities of daily living, which largely rely on the use of the less-affected ipsilesional arm. While use of the ipsilesional arm is often encouraged as a compensatory strategy in rehabilitation, substantial evidence indicates that motor control deficits in this arm can be functionally limiting, suggesting a role for remediation of this arm. Previous research has indicated that the nature of ipsilesional motor control deficits vary with hemisphere of damage and with the severity of contralesional paresis. Thus, in order to design rehabilitation that accounts for these deficits in promoting function, it is critical to understand the relative contributions of both ipsilesional and contralesional arm motor deficits to functional independence in stroke survivors with severe contralesional paresis. We now examine motor deficits in each arm of severely paretic chronic stroke survivors with unilateral damage (10 left-, 10 right-hemisphere damaged individuals) to determine whether hemisphere-dependent deficits are correlated with functional independence. Clinical evaluation of contralesional, paretic arm impairment was conducted with the upper extremity portion of the Fugl-Meyer assessment (UEFM). Ipsilesional arm motor performance was evaluated using the Jebsen-Taylor Hand Function Test (JTHFT), grip strength, and ipsilesional high-resolution kinematic analysis during a visually targeted reaching task. Functional independence was measured with the Barthel Index. Functional independence was better correlated with ipsilesional than contralesional arm motor performance in the left hemisphere damage group [JTHFT: [r(10) = −0.73, p = 0.017]; grip strength: [r(10) = 0.64, p = 0.047]], and by contralesional arm impairment in the right hemisphere damage group [UEFM: [r(10) = 0.66, p = 0.040]]. Ipsilesional arm kinematics were correlated with functional independence in the left hemisphere damage group only. Examination of hemisphere-dependent motor correlates of functional independence showed that ipsilesional arm deficits were important in determining functional outcomes in individuals with left hemisphere damage only, suggesting that functional independence in right hemisphere damaged participants was affected by other factors.