  The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome
antiferromagnet has potential instabilities[1-4]. This has been suggested as
the reason why it is not strongly supported in large-scale numerical
calculations[5]. However, previous attempts to observe these instabilities have
failed. We report on the discovery of a projected BCS state with lower energy
than the projected Dirac spin liquid state which provides new insight into the
stability of the ground state of the kagome antiferromagnet. The new state has
three remarkable features. First, it breaks both spatial symmetry in an unusual
way that may leave spinons deconfined along one direction. Second, it breaks
the U(1) gauge symmetry down to $Z_2$. Third, it has the spatial symmetry of a
previously proposed "monopole" suggesting that it is an instability of the
Dirac spin liquid. The state described herein also shares a remarkable
similarity to the distortion of the kagome lattice observed at low Zn
concentrations in Zn-Paratacamite suggesting it may already be realized in
these materials.
