First observation of the decay B-s(0) -> (D) over bar (0)phi is reported using pp collision data, corresponding to an integrated luminosity of 1.0 fb(-1), collected by the LHCb experiment at a centre-of-mass energy of 7 TeV. The significance of the signal is 6.5 standard deviations. The branching fraction is measured relative to that of the decay B-S(0) -> (D) over bar (0)phi to be beta B-S(0) -> (D) over bar (0)phi/beta B-S(0) -> (D) over bar (0)(K) over bar*(0) = 0.069 +/- 0.013 (stat) +/- 0.007 (syst). The first measurement of the ratio of branching fractions for the decays beta B-S(0) -> (D) over bar (0)(K) over bar*(0) and beta B-S(0) -> (D) over bar (0)(K) over bar*(0) is found to be beta B-S(0) -> (D) over bar (0)(K) over bar*(0/)beta B-S(0) -> (D) over bar (0)(K) over bar*(0=7.8) +/- 0.7(stat) +/- 0.3 (syst) +/- 0.6 (f(s)/f(d)) where the last uncertainty is due to the ratio of the B(s)(0)and B-0 fragmentation fractions. (C) 2013 CERN. Published by Elsevier B.V. All rights reserved.