  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 ($\sim 0.3 \%$ 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.
