  I present a formalism for dealing directly with the effects of the Gutzwiller
projection, which is implicit in the t-J model widely believed to underly the
phenomenology of the high-Tc cuprates. I suggest that a true BCS condensation
from a Fermi liquid state takes place, but in the unphysical space prior to
projection. The theory which results upon projection does not follow
conventional rules of diagram theory and in fact in the normal state is a Z=0
non-Fermi liquid. Anomalous properties of this strange metal normal state are
predicted and compared to experiments.
