We present polarimetric observations of the afterglow of gamma-ray burst (GRB) 021004, obtained with the Nordic Optical Telescope (NOT) and the Very Large Telescope (VLT) between 8 and 17 hours after the burst. Comparison among the observations shows a 45 degree change in the position angle from 9 hours after the burst to 16 hours after the burst, and comparison with published data from later epochs even shows a 90 degree change between 9 and 89 hours after the burst. The degree of linear polarization shows a marginal change, but is also consistent with being constant in time. In the context of currently available models for changes in the polarization of GRBs, a homogeneous jet with an early break time of t_b ~ 1 day provides a good explanation of our data. The break time is a factor 2 to 6 earlier than has been found from the analysis of the optical light curve. The change in the position angle of the polarization rules out a structured jet model for the GRB.
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