  We study effective field theories (EFT) of nuclear structure based on
spontaneously broken global $SU(2)_L\times SU(2)_R$ chiral symmetry of QCD with
two massless quarks, i.e. $SU(2)\chi PT$. For ground-state nuclei, this EFT
enables expansion and truncation in inverse powers of $\Lambda_{\chi SB}\simeq
1 GeV$, with analytic operators renormalized to all loop orders. We derive the
EFT Lagrangian to order $\Lambda^0_{\chi SB}$.
  We show that $SU(2)\chi PT$ of protons, neutrons and pions admits a
semi-classical "Static Chiral Nucleon Liquid" (Static$\chi$NL) phase and that
"Pion-less" $SU(2)\chi PT$ emerges in this liquid: far-infrared pions decouple
from Static$\chi$NL, vastly simplifying the derivation of saturated nuclear
matter (the infinite liquid phase) and of finite microscopic liquid drops
(ground-state nuclides).
  Static$\chi$NL are made entirely of nucleons with even parity, total spin
zero, and even $Z$ and $N$; local expectation values for spin and momenta
vanish. They explain the power of pion-less $SU(2)\chi PT$ to capture
experimental ground-state properties of certain nuclides, this explanation
following directly from the global symmetries of QCD with two massless quarks.
  Mean-field Static$\chi$NL non-topological solitons are true solutions of
$SU(2)\chi PT$'s semi-classical symmetries: they obey all CVC and PCAC
conservation laws and they have zero internal and external pressure. The
nuclear liquid-drop model and the semi-empirical mass formula emerge -- with
correct nuclear density and saturation and asymmetry energies -- in an explicit
Thomas-Fermi construction.
  We relate our work to compatible and complementary work in pionless and in
halo/ cluster EFTs, also composed entirely of nucleons and applied to light
($A\leq 6$) nuclei, which might provide important (<12.5%) corrections to
Static$\chi NL$.
