  We prove that for every graph $H$, there exists $\varepsilon>0$ such that
every $n$-vertex graph with no vertex-minors isomorphic to $H$ has a pair of
disjoint sets $A$, $B$ of vertices such that $|A|, |B|\ge \varepsilon n$ and
$A$ is complete or anticomplete to $B$. We deduce this from recent work of
Chudnovsky, Scott, Seymour, and Spirkl (2018). This proves the analog of the
Erd\H{o}s-Hajnal conjecture for vertex-minors.
