  A subset $\{g_1, \ldots , g_d\}$ of a finite group $G$ invariably generates
$G$ if $\{g_1^{x_1}, \ldots , g_d^{x_d}\}$ generates $G$ for every choice of
$x_i \in G$. The Chebotarev invariant $C(G)$ of $G$ is the expected value of
the random variable $n$ that is minimal subject to the requirement that $n$
randomly chosen elements of $G$ invariably generate $G$. Confirming a
conjecture of Kowalski and Zywina, we prove that there exists an absolute
constant $\beta$ such that $C(G) \leq \beta\sqrt{|G|}$ for all finite groups
$G.$
