  A Riemann surface $M$ is said to be $K$-quasiconformally homogeneous if for
every two points $p,q \in M$, there exists a $K$-quasiconformal homeomorphism
$f \colon M \rightarrow M$ such that $f(p) = q$. In this paper, we show there
exists a universal constant $K_0 > 1$ such that if $M$ is a
$K$-quasiconformally homogeneous hyperbolic genus zero surface other than the
disk $\mathbb{D}$, then $K \geq K_0$. This answers a question by Gehring and
Palka.
