It is generally assumed that the uniqueness of individual identity is reflected in the connective architecture of the human brain. Here we introduce local connectome fingerprinting, a noninvasive method that uses diffusion MRI to characterize white matter bundles as fingerprints. Using four independently acquired datasets (total n=213), we show that the local connectome fingerprint is highly specific to an individual, achieving 100% accuracy across 17,398 identification tests with an estimated classification error at 10-6. This uniqueness profile is higher than fingerprints derived from local fractional anisotropy or region-to-region connectivity patterns. We further illustrate that local connectome fingerprinting allows for quantifying similarity between genetically-associated individuals, e.g., monozygotic twins (12% connectomic similarity), and neuroplasticity with time, e.g., fingerprint uniqueness decreases 0.02% per day. This approach opens a new door for probing the influence of pathological, genetic, social, or environmental factors on the unique configuration of the human connectome.