  Chiral symmetry is always broken in cold, dense matter, by chiral
condensation at low densities and by diquark condensation at high density. We
construct here, within a schematic Nambu-Jona-Lasinio (NJL) model, the
corresponding generalized Nambu-Goldstone pion, $\pi_G$. As we show, the
$\pi_G$ mode naturally emerges as a linear combination of the $\langle
\bar{q}q\rangle$ vacuum pion $\pi$ and the $\langle qq \rangle$ diquark
condensate pion $\tilde{\pi}$, with $q$ the quark field, and continuously
evolves with increasing density from being $\pi$-like in the vacuum to
$\tilde{\pi}$-like in the high density diquark pairing phase. We calculate the
density-dependent mass, decay constant, and coupling to quarks of the $\pi_G$,
and derive a generalized Gell-Mann--Oakes--Renner (GMOR) relation in the
presence of a finite bare quark mass $m_q$. We briefly discuss the implications
of the results to possible Bose condensation of $\pi_G$ in more realistic
models.
