  We study a Yang-Baxter integrable quantum spin-1/2 chain with random
interactions. The Hamiltonian is local and involves two and three-spin
interactions with random parameters. We show that the energy eigenstates of the
model are never localized and in fact exhibit perfect energy and spin transport
at both zero and infinite temperatures. By considering the vicinity of a free
fermion point in the model we demonstrate that this behavior persists under
deformations that break integrability but preserve the free fermion nature of
the Hamiltonian. In this case the ballistic behavior can be understood as
arising from the correlated nature of the disorder in the model. We conjecture
that the model belongs to a broad class of models avoiding localization in 1D.
