Abstract: The (P) over bar ANDA (anti-Proton ANnihiliation at DArmstadt) experiment will be one of the four flagship experiments at the new international accelerator complex FAIR (Facility for Antiproton and Ion Research) in Darmstadt, Germany. (P) over bar ANDA will address fundamental questions of hadron physics and quantum chromodynamics using high-intensity cooled antiproton beams with momenta between 1.5 and 15 GeV/c and a design luminosity of up to 2 x 10(32) cm(-2) S-1. Excellent particle identification (PID) is crucial to the success of the (P) over bar ANDA physics program. Hadronic PID in the barrel region of the target spectrometer will be performed by a fast and compact Cherenkov counter using the detection of internally reflected Cherenkov light (DIRC) technology. It is designed to cover the polar angle range from 22 degrees to 140 degrees and will provide at least 3 standard deviations (s.d.) pi/K separation up to 3.5 GeV/c, matching the expected upper limit of the final state kaon momentum distribution from simulation. This documents describes the technical design and the expected performance of the (P) over bar ANDA Barrel DIRC detector. The design is based on the successful BaBar DIRC with several key improvements. The performance and system cost were optimized in detailed detector simulations and validated with full system prototypes using particle beams at GSI and CERN. The final design meets or exceeds the PID goal of clean pi/K separation with at least 3 s.d. over the entire phase space of charged kaons in the Barrel DIRC.