Let $G$ be a graph. Denote by $L^i(G)$ its $i$-iterated line graph and denote by $W(G)$ its Wiener index. We find an infinite class of trees $T$ satisfying $W(L^3(T))=W(T)$, which disproves a conjecture of Dobrynin and Entringer [Electronic Notes in Discrete Math. 22 (2005) 469--475].