  The spectrum of a bound state of three identical particles with a mass $m$ in
a finite cubic box is studied. It is shown that in the unitary limit, the
energy shift of a shallow bound state is given by $\Delta E=c
(\kappa^2/m)\,(\kappa L)^{-3/2}|A|^2\exp(-2\kappa L/\sqrt{3})$, where $\kappa$
is the bound-state momentum, $L$ is the box size, $|A|^2$ denotes the
three-body analog of the asymptotic normalization coefficient of the bound
state wave function and $c$ is a numerical constant. The formula is valid for
$\kappa L\gg 1$.
