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Evidence for a low-frequency stochastic gravitational wave background hasrecently been reported based on analyses of pulsar timing array data. The mostlikely source of such a background is a population of supermassive black holebinaries, the loudest of which may be individually detected in these datasets.Here we present the search for individual supermassive black hole binaries inthe NANOGrav 15-year dataset. We introduce several new techniques, whichenhance the efficiency and modeling accuracy of the analysis. The searchuncovered weak evidence for two candidate signals, one with agravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. Thesignificance of the low-frequency candidate was greatly diminished whenHellings-Downs correlations were included in the background model. Thehigh-frequency candidate was discounted due to the lack of a plausible hostgalaxy, the unlikely astrophysical prior odds of finding such a source, andsince most of its support comes from a single pulsar with a commensurate binaryperiod. Finding no compelling evidence for signals from individual binarysystems, we place upper limits on the strain amplitude of gravitational wavesemitted by such systems.

The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries