  In this short paper, we consider the Once-reinforced random walk with
reinforcement parameter $a$ on trees with bounded degree which are transient
for the simple random walk. On each of these trees, we prove that there exists
an explicit critical parameter $a_0$ such that the Once-reinforced random walk
is almost surely recurrent if $a>a_0$ and almost surely transient if $a<a_0$.
This provides the first examples of phase transition for the Once-reinforced
random walk.
