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HD 110067 is the brightest star known to have six transiting planets. Each adjacent pair of planets has a period ratio that is nearly equal to a ratio of small integers, suggesting the planets are in a chain of mean-motion resonances, but the limited time span of the available data has prevented firm conclusions. Here, we show that the requirement of long-term dynamical stability implies that all six planets are very likely to form a resonant chain. Dynamical simulations of nonresonant systems with initial conditions compatible with the available data almost always suffer an instability within 25 Myr (∼0.3% of the system’s age). Assuming the system is in resonance, we place upper limits on the planets’ eccentricities and lower limits on the masses of the planets that have not yet been measured. We also predict the characteristics of transit timing variations and the values of the three-body libration centers.