HR 8799 is a nearby star hosting at least four ~10 m Jup planets in wide orbits up to ~70 au, detected through the direct, high-contrast infrared imaging. Large companions and debris discs reported interior to ~10 au, and exterior to ~100 au 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° to the sky plane. This best-fitting orbital configuration matches astrometry, debris disc models, and mass estimates from cooling models. The multiple mean motion resonance (MMR) is stable for the age of the star ~160 Myr, 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 ~9.7 au, or ~7.5 au 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.