The "butterfly" molecule [Fe₃Y(μ3-O)₂(CCl₃COO)₈(H₂O)(THF)₃] (in brief {Fe₃YO₂}) includes three Fe³⁺ ions which build a robust Fe₃ cluster with a strong intracluster antiferromagnetic exchange and a total spin S = 5/2. It represents the starting magnetic system to study further interactions with magnetic rare earths when Y is replaced with lanthanides. We present heat capacity and equilibrium susceptibility measurements below 2 K, which show that each cluster has a sizeable magnetic anisotropy pointing to the existence of intercluster interactions. However, no phase transition to a long-range magnetically ordered phase is observed down to 20 mK. The intercluster interaction is analysed in the framework of the one-dimensional Blume-Capel model with an antiferromagnetic chain interaction constant J/k_B = -40(2) mK between Fe₃ cluster spins, and a uniaxial anisotropy with parameter D/k_B = -0.56(3) K. This is associated to single chains of Fe₃ clusters oriented along the shortest intercluster distances displayed by the crystal structure of {Fe₃YO₂}. Ac susceptibility measurements reveal that the magnetic relaxation is dominated by a quantum tunnelling process below 0.2 K, and by thermally activated processes above this temperature. The experimental activation energy of this single chain magnet, E_a/k_B = 3.4(6) K, can be accounted for by the combination of contributions arising from single-molecule magnetic anisotropy and spin-spin correlations along the chains.