  Evidence for a low-frequency stochastic gravitational wave background has
recently been reported based on analyses of pulsar timing array data. The most
likely source of such a background is a population of supermassive black hole
binaries, the loudest of which may be individually detected in these datasets.
Here we present the search for individual supermassive black hole binaries in
the NANOGrav 15-year dataset. We introduce several new techniques, which
enhance the efficiency and modeling accuracy of the analysis. The search
uncovered weak evidence for two candidate signals, one with a
gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The
significance of the low-frequency candidate was greatly diminished when
Hellings-Downs correlations were included in the background model. The
high-frequency candidate was discounted due to the lack of a plausible host
galaxy, the unlikely astrophysical prior odds of finding such a source, and
since most of its support comes from a single pulsar with a commensurate binary
period. Finding no compelling evidence for signals from individual binary
systems, we place upper limits on the strain amplitude of gravitational waves
emitted by such systems.
