  In this paper, we study the hypercyclicity of forward and backward shifts on
weighted $L^p$ spaces of a directed tree. In the forward case, only the trivial
trees may support hypercyclic shifts, in which case the classical results of
Salas apply. For the backward case, nontrivial trees may support hypercyclic
shifts. We obtain necessary conditions and sufficient conditions for
hypercyclicity of the backward shift and, in the case of a rooted tree on an
unweighted space, we show that these conditions coincide.
