The decay B(s)(0) → J/ψK+ K- is investigated using 0.16 fb(-1) of data collected with the LHCb detector using 7 TeV pp collisions. Although the J/ψϕ channel is well known, final states at higher K+ K- masses have not previously been studied. In the K+ K- mass spectrum we observe a significant signal in the f(2)'(1525) region as well as a nonresonant component. After subtracting the nonresonant component, we find B(B(s)(0) → J/ψf(2)'(1525))/B(B(s)(0) → J/ψϕ) = (26.4 ± 2.7 ± 2.4)%.