  An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is
said to be isometric if the row operator $(V_1,...,V_n) : H^n \to H$ is an
isometry. We prove that every isometric $n$-tuple is hyperreflexive, in the
sense of Arveson. For $n = 1$, the hyperreflexivity constant is at most 95. For
$n \geq 2$, the hyperreflexivity constant is at most 6.
