We investigate superconducting granular aluminum (grAl) as a promising material for quantum circuits. We show that grAl strips can reach kinetic inductances up to nH/sq, while maintaining small microwave frequency losses. We identify excess quasiparticles as a limiting loss mechanism, and find quasiparticle relaxation times on the order of seconds. By fabricating a fluxonium quantum bit with a grAl superinductor, we demonstrate that grAl is a viable material for superconducting quantum circuits.