Quasicrystals are non-periodic, yet they exhibit long-range order resulting from the underlying deterministic construction principle and allow Bragg diffraction. We propose a resonant one-dimensional quasicrystal, namely, a multiple quantum well (MQW) structure satisfying the Fibonacci-chain rule with the golden ratio between the long and short interwell distances. The resonant Bragg condition is generalized from the periodic to Fibonacci MQWs. A dispersion equation for exciton polaritons is derived in the two-wave approximation; the effective allowed and forbidden bands are found. The reflection spectra from the proposed structures are calculated and compared with experiment.

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