  Let $k$ be a perfect field of virtual cohomological dimension $\leq 2$. Let
$G$ be a connected linear algebraic group over $k$ such that $G^{sc}$ satisfies
a Hasse principle over $k$. Let $X$ be a principal homogeneous space under $G$
over $k$. We show that if $X$ admits a zero cycle of degree one, then $X$ has a
$k$-rational point.
