The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time $O(n^4)$ whether three given vertices of a graph belong to an induced tree. Here, we study four-in-a-tree for triangle-free graphs. We give a structural answer to the following question: how does look like a triangle-free graph such that no induced tree covers four given vertices~? Our main result says that any such graph must have the ``same structure'', in a sense to be defined precisely, as a square or a cube. We provide an $O(nm)$-time algorithm that given a triangle-free graph~$G$ together with four vertices outputs either an induced tree that contains them or a partition of $V(G)$ certifying that no such tree exists. We prove that the problem of deciding whether there exists a tree $T$ covering the four vertices such that at most one vertex of $T$ has degree at least~3 is NP-complete.