  We give a construction of an odd spectral triple on the Cuntz algebra
$O_{N}$, whose $K$-homology class generates the odd $K$-homology group
$K^1(O_{N})$. Using a metric measure space structure on the Cuntz-Renault
groupoid, we introduce a singular integral operator which is the formal
analogue of the logarithm of the Laplacian on a Riemannian manifold. Assembling
this operator with the infinitesimal generator of the gauge action on $O_{N}$
yields a $\theta$-summable spectral triple whose phase is finitely summable.
The relation to previous constructions of Fredholm modules and spectral triples
on $O_{N}$ is discussed.
