The first observation of the decay B0→D¯(0)K(+)K(-) is reported from an analysis of 0.62 fb(-1) of pp collision data collected with the LHCb detector. Its branching fraction is measured relative to that of the topologically similar decay B(0)→D ¯(0)π(+)π(-) to be (B(B(0)→D¯(0)K(+)K(-))/B(B(0)→D¯(0)π(+)π(-))=0.056±0.011±0.007,where the first uncertainty is statistical and the second is systematic. The significance of the signal is 5.8σ. Evidence, with 3.8σ significance, for B(s)(0)→D¯(0)K(+)K(-) decays is also presented. The relative branching fraction is measured to be B(B(s)(0)→D¯(0)K(+)K(-))/B(B(0)→D¯(0)K(+)K(-))=0.90±0.27±0.20. These channels are of interest to study the mechanisms behind hadronic B decays, and open new possibilities for CP violation analyses with larger data sets.