We systematically explore the stability and properties of [B12X11NG]- adducts resulting from the binding of noble gas atoms to anionic [B12X11]- clusters in the gas phase of mass spectrometers. [B12X11]- can be obtained by stripping one X- off the icosahedral closo-dodecaborate dianion [B12X12]2-. We study the binding of the noble gas atoms He, Ne, Ar, Kr, and Xe to [B12X11]- with substituents X = F, Cl, Br, I, and CN. While He cannot be captured by these clusters and Ne only binds at low temperatures, the complexes with the heavier noble gas atoms Ar, Kr, and Xe show appreciable complexation energies and exceed 1 eV at room temperature in the case of [B12(CN)11Xe]-. The predicted B-NG equilibrium distance in the complexes with Ar, Kr, and Xe is only 0.10-0.25 Å longer than the sum of the covalent radii of the two corresponding atoms, and a significant charge transfer from the noble gas atom to the icosahedral B12 cage is observed.