Results are presented of early X-ray afterglow observations of GRB 060105 by Swift and Suzaku. The bright, long gamma-ray burst GRB 060105 triggered the Swift Burst Alert Telescope (BAT) at 06:49:28 on 5 January 2006. The Suzaku team commenced a pre-planned target of opportunity observation at 19 ks (5.3 hr) after the Swift trigger. Following the prompt emission and successive very steep decay, a shallow decay was observed from T_0+187 s to T_0+1287 s. After an observation gap during T_0 +(1.5-3) ks, an extremely early steep decay was observed in T_0+(4-30) ks. The lightcurve flattened again at T_0+30 ks, and another steep decay followed from T_0+50 ks to the end of observations. Both steep decays exhibited decay indices of 2.3 - 2.4. This very early break, if it is a jet break, is the earliest case among X-ray afterglow observations, suggesting a very narrow jet whose opening angle is well below 1 degree. The unique Suzaku/XIS data allow us to set very tight upper limits on line emission or absorption in this GRB. For the reported pseudo-redshift of z=4.0+/-1.3 the upper limit on the iron line equivalent width is 50 eV.
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