  The spin-1/2 kagome lattice antiferromagnet herbertsmithite,
ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, is a candidate material for a quantum spin liquid
ground state. We show that the magnetic response of this material displays an
unusual scaling relation in both the bulk ac susceptibility and the low energy
dynamic susceptibility as measured by inelastic neutron scattering. The
quantity $\chi T^\alpha$ with $\alpha \simeq 0.66$ can be expressed as a
universal function of $H/T$ or $\omega/T$. This scaling is discussed in
relation to similar behavior seen in systems influenced by disorder or by the
proximity to a quantum critical point.
