  We study the Localization game on locally finite graphs trees, where each of
the countably many vertices have finite degree. In contrast to the finite case,
we construct a locally finite tree with localization number $n$ for any choice
of positive integer $n$. Our examples have uncountably many ends, and we show
that this is necessary by proving that locally finite trees with finitely or
countably many ends have localization number at most 2. Finally, as is the case
for finite graphs, we prove that any locally finite graph contains a
subdivision where one cop can capture the robber.
