Despite the success of multiple-port minimally invasive intervention (MII) systems, current research is fast moving away from standard, kinematically rigid MII instruments toward more flexible, highly articulated devices, such as robotic catheters, probes, and forceps. These new devices afford surgeons the same dexterity and range of motion as multiple-port systems while using only a single incision. Single-port MII devices hold the promise of facilitating procedures in small, geometrically complex spaces, such as those seen cardiothoracic surgery, with even lower risks of infection and patient discomfort than possible with multiple-port systems. However, the mechanical sophistication of these robotic devices requires careful consideration of morphological design to ensure that the complexity and cost of design is not economically prohibitive enough to outweigh the clinical benefits of improved robot flexibility. This study focuses on the intelligent design of a kinematically redundant, single-port MII robot architecture by way of morphological optimization. This MII device morphology is optimized to access the cardiothoracic cavity through a single 12 mm subxiphoid port and reach several regions of interest, consistent with procedures such as epicardial ablation and therapeutic substance injection, with minimal physiologic disturbance. The optimization process employs a recently developed morphological fitness metric to measure a candidate morphology's ability to navigate the cardiothoracic environment and perform surgical maneuvers with high end-effector flexibility while maintaining safe distances from anatomical structures. This fitness metric uses a Jacobian-based formulation to quantify a robot's capacity to avoid collisions with motion impediments and to minimize the mechanical torque required for the intended task. In addition to performance-based criterion, this optimization process also considers design factors such as part manufacturability and expense which heavily influence economic feasibility. Morphological optimization is performed by searching the mechanical design parameter space, which consists of part dimensions and linkage types, using genetic algorithms. The execution of specific surgical maneuvers is simulated for each candidate morphology until the fitness metric is maximized. Final simulations of the optimized device morphology working in the cardiothoracic cavity are performed to demonstate the functional advantages of the optimized single-port robot over current multiple-port systems.