I've heard the story a thousand times but I haven't been able to verify it. He's long dead now, but the story goes that he was at some kind of golf tournament in California (not a pro tournament, because he certainly wasn't that, but some other sort). There were supposedly a bunch of "important" people there.
The story goes that on one hole he hit a great shot and got a hole in one. After the celebration, one of his playing partners said he bets he could never do it again. T. Earl said something like, "well, let's find out!" and put down another ball. That ball, too, went in the hole, right on top of the first one. Two swings in a row.
My family said they had the newspaper article about it for years. It happened in california somewhere. I haven't been able to verify it but I'd love to track down that newspaper article. The way my older family members talked about it, and with the many witnesses and the supposed article in the newspaper, I tend to believe it.