Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, about 100 Omega, and small anharmonicity, which can limit their coherence and logic gate fidelity(1,2). A promising alternative is circuits based on so-called superinductors(3-6), with characteristic impedances exceeding the resistance quantum R-Q = 6.4 k Omega. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays(7,8), can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here, we present a fluxonium qubit design based on a granular aluminium superinductor strip(9-11). We show that granular aluminium can form an effective junction array with high kinetic inductance and be in situ integrated with standard aluminium circuit processing. The measured qubit coherence time T-2* <= 30 mu s illustrates the potential of granular aluminium for applications ranging from protected qubit designs to quantum-limited amplifiers and detectors.