  HR 8799 is a nearby star hosting at least four ~10 Jovian mass planets in
wide orbits up to ~70au, detected through the direct, high-contrast infrared
imaging. Large companions and debris disks reported interior to ~10au, and
exterior to ~100au indicate massive protoplanetary disc in the past. The
dynamical state of the HR 8799 system is not yet fully resolved, due to limited
astrometric data covering tiny orbital arcs. We construct a new, orbital model
of the HR 8799 system, assuming rapid migration of the planets after their
formation in wider orbits. We found that the HR 8799 planets are likely
involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary
orbits are coplanar with the stellar equator and inclined by ~25 degrees to the
sky plane. This best-fit orbital configuration matches astrometry, debris disk
models, and mass estimates from cooling models. The multiple MMR is stable for
the age of the star ~160Myr, for at least 1 Gyr unless significant
perturbations to the N-body dynamics are present. We predict four
configurations with the fifth hypothetical innermost planet HR 8799f in ~9.7au,
or ~7.5au orbit, extending the MMR chain to triple Laplace resonance
1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings
may establish strong boundary conditions for the system formation and its early
history.
