We perform a full dynamic inversion at low frequencies of the 16 December 2007 (Mw = 6.7) northern Chile earthquake that we model as a simple elliptical patch. We use two different stress-friction end-member models: asperities and barriers, finding similar results. The inversions are performed for strong motion data filtered between 0.02 and 0.5 Hz. Eleven geometrical and stress and friction parameters are inverted using the neighbourhood algorithm. The optimum solutions have relative errors lower than 0.21. The earthquake rupture has duration of less than 5 s and propagates at sub-shear speed. The rupture area is similar to that of the aftershock distribution and the seismic moment is 0.95 . 10(19) Nm. We derive the friction law parameters from the models situated close to the optimum solution using a Monte Carlo technique. The results show a strong trade-off between applied stress and frictional resistance. We find that the distribution of friction models collapses into a finite zone of the space of moment and non-dimensional parameter kappa. We conclude that it is possible to determine the friction law from near field seismograms, but there is a strong trade-off between friction and initial stress. Citation: Ruiz, S., and R. Madariaga (2011), Determination of the friction law parameters of the Mw 6.7 Michilla earthquake in northern Chile by dynamic inversion, Geophys. Res. Lett., 38, L09317, doi: 10.1029/2011GL047147.