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From heavy fermion compounds and cuprates to iron pnictides and chalcogenides, a spin resonance at 􏰀Ω0 ∝ 𝑘B𝑇c is a staple of nearly magnetic superconductors. Possible explanations include a two-particle bound state or loss of magnon damping in the superconducting state. While both scenarios suggest a central role for magnetic fluctuations, distinguishing them is important to identify the right theoretical framework to understand these types of unconventional superconductors. Using an inelastic neutron scattering technique, we show that the spin resonance in the optimally doped Fe1.03Se0.4Te0.6 superconductor splits into three peaks in a high magnetic field, a signature of a two-particle 𝑆 = 1 triplet bound state.