The 40-year-old sank five birdies, including two in the final three holes.
That put him behind only American duo Shawn Stefani and Tom Hoge, and Korean Seung-yul Noh.
Miguel Angel Carballo, Brian Gay, Colt Knost, Dustin Johnson and Steve Stricker matched Donaldson, with Retief Goosen among those a further shot back.
This is the final PGA Tour event before the US Open - the second major of the year - takes place at Oakmont next week.
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Welshman Jamie Donaldson shot a four-under-par 66 to sit one behind the leaders after the first round of the St Jude Classic at TPC Southwind.