The simultaneous suppression of charge fluctuations and offsets is crucial for preserving quantum coherence in devices exploiting large quantum fluctuations of the superconducting phase. This requires an environment with both extremely low DC and high RF impedance. Such an environment is provided by a superinductance, defined as a zero DC resistance inductance whose impedance exceeds the resistance quantum $R_Q = h/(2e)^2 ≃ 6.5\ \mathrm{k\Omega}$ at frequencies of interest (1 - 10 GHz). In addition, the superinductance must have as little dissipation as possible, and possess a self-resonant frequency well above frequencies of interest. The kinetic inductance of an array of Josephson junctions is an ideal candidate to implement the superinductance provided its phase slip rate is sufficiently low. We successfully implemented such an array using large Josephson junctions ($E_J >> E_C$), and measured internal losses less than 20 ppm, self-resonant frequencies greater than 10 GHz, and phase slip rates less than 1 mHz.