The ammonioborane monoanion H(3)NB(12)H(11)(-) was per-B-fluorinated with elemental fluorine in liquid hydrogen fluoride to yield the first member of a new class of weakly coordinating anions, H(3)NB(12)F(11)(-) (isolated as [N(n-Bu)(4)](2)[H(2)NB(12)F(11)] in 41% yield). The pK(a) of the H(3)NB(12)F(11)(-) anion is 9.6. Several salts of the tri-N-alkylated anions Me(3)NB(12)F(11)(-) and Dd(3)NB(12)F(11)(-) (Dd = n-C(12)H(25)) were also prepared. The structure of [CPh(3)][Me(3)NB(12)F(11)] was determined by single-crystal X-ray diffraction: monoclinic, space group P2(1)/c, a = 18.053(3) A, b = 33.139(5) A, c = 9.600(2) A, beta = 91.459(4) degrees, V = 5742(2) A(3), Z = 8, T = 173(2) K, R(1) = 0.045. It revealed that the only direct interactions between the undecafluoroammonioborate monoanions and the trityl cations in the two independent ion pairs were long and weak BF...CPh(3) interactions of 2.992(6) and 2.942(6) A. Salts of the new anions were chemically, electrochemically, and thermally stable. The conductivity of Li(Me(3)NB(12)F(11)) in dimethoxyethane was comparable to that of LiPF(6) but less than half the value of Li(1-Me-CB(11)F(11)).