The first observation of the decay B s 0 ->χ c 1 φ and a study of B 0 ->χ c 1 , 2 K 0 decays are presented. The analysis is performed using a dataset, corresponding to an integrated luminosity of 1.0 fb - 1 , collected by the LHCb experiment in pp collisions at a centre-of-mass energy of 7 TeV. The following ratios of branching fractions are measured:B(B s 0 ->χ c 1 φ)B(B s 0 ->J/ψφ)=(18.9+/-1.8 (stat) +/-1.3 (syst) +/-0.8(B))x10 - 2 ,B(B 0 ->χ c 1 K 0 )B(B 0 ->J/ψK 0 )=(19.8+/-1.1 (stat) +/-1.2 (syst) +/-0.9(B))x10 - 2 ,B(B 0 ->χ c 2 K 0 )B(B 0 ->χ c 1 K 0 )=(17.1 +/-5.0(stat)+/-1.7(syst)+/-1.1(B))x10 - 2 , where the third uncertainty is due to the limited knowledge of the branching fractions of χ c ->J/ψγ modes.