  We present the theory of an extremely correlated Fermi liquid (ECFL) with
$U\to \infty$. This liquid has an underlying Fermi liquid (FL) Greens function
that is further caparisoned. The theory leads to two parallel hierarchies of
equations that permit iterative approximations in a certain parameter.
Preliminary results for the spectral functions display a broad background and a
distinct $T$ dependent left skew. An important energy scale $\Delta(\vec{k},x)$
emerges as the average inelasticity of the FL Greens function, and influences
the photoemission spectra profoundly. A duality is identified wherein an
apparent loss of coherence of the ECFL results from an excessively sharp FL.
