  Conventional heavy Fermi liquid phases of Kondo lattices involve the
formation of a "Kondo singlet" between the local moments and the conduction
electrons. This Kondo singlet is usually taken to be in an internal s-wave
angular momentum state. Here we explore the possibility of phases where the
Kondo singlet has internal angular momentum that is d-wave. Such states are
readily accessed in a slave boson mean field formulation, and are energetically
favorable when the Kondo interaction is between a local moment and an electron
at a nearest neighbor site. The properties of the d-wave Kondo liquid are
studied. Effective mass and quasiparticle residue show large angle dependence
on the Fermi surface. Remarkably in certain cases, the quasiparticle residue
goes to zero at isolated points (in two dimensions) on the Fermi surface. The
excitations at these points then include a free fractionalized spinon. We also
point out the possibility of quantum Hall phenomena in two dimensional Kondo
{\em insulators}, if the Kondo singlet has complex internal angular momentum.
We suggest that such d-wave Kondo pairing may provide a useful route to
thinking about correlated Fermi liquids with strong anisotropy along the Fermi
surface.
