Experiment and theory both suggest that the AAA-DDD pattern of hydrogen bond acceptors (A) and donors (D) is the arrangement of three contiguous hydrogen bonding centers that results in the strongest association between two species. Murray and Zimmerman prepared the first example of such a system (complex 3 circle 2) and determined the lower limit of its association constant (K-a) in CDCl3 to be 10(5) M-1 by H-1 NMR spectroscopy (Murray, T. J.; Zimmerman, S. C. J Am. Chem. Soc. 1992, 114, 4010-4011). The first cationic AAA-DDD pair (3 circle 4(+)) was described by Bell and Anslyn (Bell, D. A.; Anslyn, E. A. Tetrahedron 1995, 51, 7161-7172), with a K-a > 5 x 10(5) M-1 in CH2Cl2 as determined by UV-vis spectroscopy. We were recently able to quantify the strength of a neutral AAA-DDD arrangement using a more chemically stable AAA-DDD system, 6 circle 2, which has an association constant of 2 x 10(7) M-1 in CH2Cl2 (Djurdjevic, S.; Leigh, D. A.; McNab, H.; Parsons, S.; Teobaldi, G.; Zerbetto, F. J. Am. Chem. Soc. 2007, 129, 476-477). Here we report on further AA(A) and DDD partners, together with the first precise measurement of the association constant of a cationic AAA-DDD species. Complex 6 circle 10(+)[B(3,5-(CF3)(2)C6H3)(4)(-)] has a K-a = 3 x 10(10) M-1 at RT in CH2Cl2, by far the most strongly bound triple hydrogen bonded system measured to date. The X-ray crystal structure of 6 circle 10(+) with a BPh4- counteranion shows a planar array of three short (N (H) under bar center dot center dot center dot (N) under bar distances 1.95-2.15 angstrom), parallel (but staggered rather than strictly linear; N-H center dot center dot center dot N angles 165.4-168.8 degrees), primary hydrogen bonds. These are apparently reinforced, as theory predicts, by close electrostatic interactions (N (H) under bar- center dot -(N) under bar distances 2.78-3.29 angstrom) between each proton and the acceptor atoms of the adjacent primary hydrogen bonds.