  We call an abelian variety over a finite field $\mathbb{F}_q$ super-isolated
if its ($\mathbb{F}_q$-rational) isogeny class contains a single isomorphism
class. In this paper, we use the Honda-Tate theorem to characterize
super-isolated ordinary simple abelian varieties by certain algebraic integers.
Our main result is that for a fixed dimension $g \geq 3$, there are finitely
many such varieties.
