  Two graphs $G$ and $H$ are hypomorphic if there exists a bijection $\varphi
\colon V(G) \rightarrow V(H)$ such that $G - v \cong H - \varphi(v)$ for each
$v \in V(G)$. A graph $G$ is reconstructible if $H \cong G$ for all $H$
hypomorphic to $G$.
  It is well known that not all infinite graphs are reconstructible. However,
the Harary-Schwenk-Scott Conjecture from 1972 suggests that all locally finite
trees are reconstructible.
  In this paper, we construct a counterexample to the Harary-Schwenk-Scott
Conjecture. Our example also answers four other questions of Nash-Williams,
Halin and Andreae on the reconstruction of infinite graphs.
