The lifetime of the ( 15 2 1 − ) state of 135Te has been measured to be τ = 809(22) ps, corresponding to a reduced transition rate of B ( E 2 ; 15 2 1 − → 11 2 1 − ) =6.6(2) W.u. The experiment was performed at the focal point of the Lohengrin spectrometer and s-delayed γ rays from mass-selected A = 135 ions were detected by four LaBr3(Ce) scintillators. This allowed the fast-timing technique to be used to access lifetimes in the 10s-of-ps to ns time region. The B ( E 2 ; 15 2 1 − → 11 2 1 − ) value is typical of a vibrational transition, despite 135Te possessing only one valence neutron and two valence protons. Shell model calculations performed with the jj 56 pnb state-of-the-art effective interaction predict a B(E2) value close to the experimental one and show that contributions from the π(g7/2, d5/2) f7/2 couplings are coherent.