We report a computer-simulation study of the crystal nucleation barrier and the structure of crystal nuclei in a Lennard-Jones system at moderate supercooling. The stable structure of the Lennard-Jones solid is known to be face-centered cubic. We find that the precritical nuclei are predominantly body centered cubic ordered. But, as the nucleus grows to its critical size, the core becomes fcc ordered. Surprisingly, however, the interface of the critical nucleus retains a high degree of bcc-like ordering.