Human functional MRI (fMRI) research primarily focuses on analyzing data averaged across groups, which limits the detail, specificity, and clinical utility of fMRI resting-state functional connectivity (RSFC) and task-activation maps. To push our understanding of functional brain organization to the level of individual humans, we assembled a novel MRI dataset containing 5 hr of RSFC data, 6 hr of task fMRI, multiple structural MRIs, and neuropsychological tests from each of ten adults. Using these data, we generated ten high-fidelity, individual-specific functional connectomes. This individual-connectome approach revealed several new types of spatial and organizational variability in brain networks, including unique network features and topologies that corresponded with structural and task-derived brain features. We are releasing this highly sampled, individual-focused dataset as a resource for neuroscientists, and we propose precision individual connectomics as a model for future work examining the organization of healthy and diseased individual human brains.