The 39-year-old won two of his three Open titles at the Old Course, but was not part of the birdie party many others were enjoying today as he carded his highest ever first-round score in The Open.
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The American started with two bogeys and further dropped shots followed at the fifth, seventh and 10th before his first birdie of the day at the par-five 14th.
Woods was playing with Louis Oosthuizen, who won The Open when it was last held at St Andrews in 2010.
The South African finished in a tie for second at last month's US Open and put himself in contention for back-to-back wins at St Andrews with a five-under 67.
The third member of Woods's group was Australian Jason Day, who is one shot off Johnson's lead thanks to a round of 66.