  Experimental evidence for a plethora of low energy spin excitations in the
spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2 may be understandable in terms of
an extended Fermi surface of spinons coupled to a U(1) gauge field. We carry
out variational calculations to examine the possibility that such a state may
be energetically viable. A Gutzwiller-projected wavefunction reproduces the
dimerization of a kagome strip found previously by DMRG. Application to the
full kagome lattice shows that the inclusion of a small ferromagnetic
next-nearest-neighbor interaction favors a ground state with a spinon Fermi
surface.
