It is known that the nonlinearity of interatomic interactions can ensure the existence of spatially localized vibrational modes in the crystal lattice. In the present work, we investigate a one-dimensional nonlinear vibrational mode of a new type in a defect-free FCC single crystal. In this mode, the atoms of one close-packed series oscillate with the same amplitude in antiphase with the nearest neighbors. The amplitudes of atomic vibrations in neighboring close-packed chains are much smaller and decrease rapidly with distance from the excited chain. The considered vibrational mode can be classified as a discrete breather (DB) of a special form, in which the oscillations are localized in two spatial directions and are delocalized in the third direction (along a close-packed atomic row). The obtained results broaden our understanding of the nonlinear dynamics of the crystal lattice of FCC metals