The rupture process of the 2014 Iquique, Chile earthquake is inverted from teleseismic P wave data applying a novel formulation that takes into account the uncertainty of Green's function, which has been a major error source in waveform inversion. The estimated seismic moment is 1.5 x 10(21) Nm (Mw=8.1), associated with a 140 km long and 140 km wide fault rupture along the plate interface. The source process is characterized by unilateral rupture propagation. During the first 20 s, the dynamic rupture front propagated from the hypocenter to the large asperity located about 50 km southward, crossing a remarkably active foreshock area at high velocity (of about 3.0 km/s), but small and irregular seismic moment release rate. Our result may suggest that the 20 s long initial phase was influenced by the stress drop due to the foreshock activity near the main shock hypocenter. Moreover, the 2 week long swarm-like foreshock activity migrating roughly at 5 km/day toward the main shock hypocenter, and possibly associated slow slip, contributed to the stress accumulation prior to the Mw 8.1 megaquake. The main shock initial rupture phase might have triggered the rupture of the large asperity, which had large fracture energy.