  Surveys have revealed many multi-planet systems containing super-Earths and
Neptunes in orbits of a few days to a few months. There is debate whether in
situ assembly or inward migration is the dominant mechanism of the formation of
such planetary systems. Simulations suggest that migration creates tightly
packed systems with planets whose orbital periods may be expressed as ratios of
small integers (resonances), often in a many-planet series (chain). In the
hundreds of multi-planet systems of sub-Neptunes, more planet pairs are
observed near resonances than would generally be expected, but no individual
system has hitherto been identified that must have been formed by migration.
Proximity to resonance enables the detection of planets perturbing each other.
Here we report transit timing variations of the four planets in the Kepler-223
system, model these variations as resonant-angle librations, and compute the
long-term stability of the resonant chain. The architecture of Kepler-223 is
too finely tuned to have been formed by scattering, and our numerical
simulations demonstrate that its properties are natural outcomes of the
migration hypothesis. Similar systems could be destabilized by any of several
mechanisms, contributing to the observed orbital-period distribution, where
many planets are not in resonances. Planetesimal interactions in particular are
thought to be responsible for establishing the current orbits of the four giant
planets in the Solar System by disrupting a theoretical initial resonant chain
similar to that observed in Kepler-223.
