The Coulomb excitation of backscattered llB projectiles has been used to measure the reduced E2 transition probability B(E2; 3/2--+ 1/2-) between the 3/2-ground state and the 1/2-first excited state of llB. It is found that B(E2;3/2--+1/2-) = 2·1±0·4 e 2 fm4, which agrees with shell model predictions but is a factor of 10 larger than the prediction of the core-excitation model.