  Bilayer quantum Hall system at total filling factor $\nu=1$ shows a rich
variety of broken symmetry ground states because of the competition between the
interlayer and intralayer Coulomb interactions. When the layers are
sufficiently close, a bilayer system develops spontaneous interlayer
phase-coherence that manifests itself through a spectacular enhancement of the
zero-bias interlayer tunneling conductance. We present a theory of this
tunneling conductance anomaly, and show that the zero-bias conductance is
proportional to the square of the {\it quasiparticle} tunneling amplitude.
