In the solid 4He at zero temperature, there are the acoustic waves, which manifest themselves in the form of phonon pairs. We show that the phonon system in solid 4He can undergo the Bardeen–Cooper–Schrieffer (BCS) condensation. In the BCS condensation state, the phonon system possesses a new kind of quasiparticle, the dressed phonon, whose velocity is a monotonically increasing function of temperature. The phonon system undergoes a first-order phase transition from the normal state to the BCS condensation state. We derive the low-temperature expression of the phonon heat capacity in the BCS condensation state, which considerably deviates from the Debye [Formula: see text] law in classic solids.