Using a dataset corresponding to an integrated luminosity of 3.0 fb(-1) collected in pp collisions at centre-of-mass energies of 7 and 8 TeV, the B (s) (0) -> aEuro parts per thousand I center dot I center dot branching fraction is measured to be B(B-0 -> phi phi) = (1.84 +/- 0.05(stat) +/- 0.07 (syst) +/- 0.11 (f(s)/f(d)) +/- 0.12 (norm)) x 10(-5) where f (s) /f (d) represents the ratio of the B (s) (0) to B (0) production cross-sections, and the B (0) -> I center dot K (*)(892)(0) decay mode is used for normalization. This is the most precise measurement of this branching fraction to date, representing a factor five reduction in the statistical uncertainty compared with the previous best measurement. A search for the decay B (0) -> I center dot I center dot is also made. No signal is observed, and an upper limit on the branching fraction is set as B(B-0 -> phi phi < 2.8 x 10(-8)) at 90% confidence level. This is a factor of seven improvement compared to the previous best limit.