  For a complex algebraic variety $X$, we show that triviality of the sheaf
cohomology group $H^0(X,\mathcal{H}^3)$ occurring on the second page of the
Bloch-Ogus spectral sequence follows from a condition on the integral Chow
group $CH^2X$ and the integral cohomology group $H^3(X, Z)$. In the case that
$X$ is an appropriate approximation to the classifying stack $BG$ of a finite
$p$-group $G$, this result states that the group $G$ has no degree three
cohomological invariants. As a corollary we show that the nonabelian groups of
order $p^3$ for odd prime $p$ have no degree three cohomological invariants.
