The folks over at XDA have successfully gained root access to the Samsung Galaxy S III. According to the article, developer Chainfire was able to successfully gain root access the SGS3. However, he is unable to publicly release the hack for fear it might be traced to the leaker.
Unlike its predecessor the Samsung Galaxy S II, the SGS3 did not show a triangle warning on boot-up, a sign that the unit is running on a modified kernel. The kernel flash counter did increase, however, and there is no known method of resetting it as of yet.
Head over to XDA for the full article: Root Achieved on the Samsung Galaxy S III