We report superconducting fluxonium qubits with coherence times largely limited by energy relaxation and reproducibly satisfying T-2 > 100 mu s (T-2 > 400 mu s in one device). Moreover, given the state-of-the-art values of the surface loss tangent and the 1/f flux-noise amplitude, the coherence time can be further improved beyond 1 ms. Our results violate a common viewpoint that the number of Josephson junctions in a superconducting circuit-over 10(2) here-must be minimized for best qubit coherence. We outline how the unique to fluxonium combination of long coherence time and large anharmonicity can benefit both gate-based and adiabatic quantum computing.