The only known qubit states that produce maximal quantum violation of a tight Bell inequality with maximally incompatible local measurements are Bell states, Greenberger-Horne-Zeilinger states, and a recently identified three-qubit state called vertical bar S >. Here we report the results of an experiment for preparing vertical bar S > and testing the maximum quantum violation of the corresponding tripartite Bell inequality. Using a heralded source of three entangled photons and three tunable polarization-dependent filters, we experimentally prepare vertical bar S > with 0.924 fidelity. Using maximally incompatible measurements for the three parties, we observe a value of T-26 = 7.30 +/- 0.06, which clearly violates the tight Bell inequality T-26 <= 5. In addition, we show that our setup allows preparing multipartite states that were inaccessible with previous methods and are useful for quantum information and metrology.