Connectome fingerprinting—a method that uses many thousands of functional connections in aggregate to identify individuals—holds promise for individualized neuroimaging. A better characterization of the features underlying successful fingerprinting performance—how many and which functional connections are necessary and/or sufficient for high accuracy—will further inform our understanding of uniqueness in brain functioning. Thus, here we examine the limits of high-accuracy individual identification from functional connectomes. Using ∼3,300 scans from the Human Connectome Project in a split-half design and an independent replication sample, we find that a remarkably small “thin slice” of the connectome—as few as 40 out of 64,620 functional connections—was sufficient to uniquely identify individuals. Yet, we find that no specific connections or even specific networks were necessary for identification, as even small random samples of the connectome were sufficient. These results have important conceptual and practical implications for the manifestation and detection of uniqueness in the brain.