  We consider the motion of a Brownian particle in $\mathbb{R}$, moving between
a particle fixed at the origin and another moving deterministically away at
slow speed $\epsilon>0$. The middle particle interacts with its neighbours via
a potential of finite range $b>0$, with a unique minimum at $a>0$, where
$b<2a$. We say that the chain of particles breaks on the left- or right-hand
side when the middle particle is greater than a distance $b$ from its left or
right neighbour, respectively. We study the asymptotic location of the first
break of the chain in the limit of small noise, in the case where $\epsilon =
\epsilon(\sigma)$ and $\sigma>0$ is the noise intensity.
