Accurate and reliable neutron capture cross sections are needed in many research areas, including stellar nucleosynthesis, advanced nuclear fuel cycles, waste transmutation, and other applied programs. In particular, the accurate knowledge of 234U(n,γ) reaction cross section is required for the design and realization of nuclear power stations based on the thorium fuel cycle. We have measured the neutron capture cross section of 234U at the recently constructed neutron time-of-flight facility n_TOF at CERN  in the energy range from 0.03 eV to 1 MeV with high accuracy due to a combination of features unique in the world: A high instantaneous neutron fluence and excellent energy resolution of the n_TOF facility, an innovative Data Acquisition System based on flash ADCs  and the use of a high performance 4π BaF2 Total Absorption Calorimeter (TAC) as a detection device [4,5], In this paper, we will describe the experimental apparatus including the various TAC components and its performance. We also will present results from the 234U(n,γ) measurement. A sample of 38.7 mg of 234U3O8 was pressed into a pellet and doubly encapsulated between Al and Ti foils which were 0.15 mm and 0.2 mm thick, respectively. Monte-Carlo simulations with GEANT4  of the detector response have been performed. After the background subtraction and correction with dead time and pile-up, the capture yield from 0.03 eV up to 1.5 keV was derived. Preliminary analysis of the capture yield in terms of R-matrix resonance parameters is discussed.