"I asked 15 or so well-connected people in the local tech community to talk about what trends, people and companies we should watch in 2001...Trends: There will be more serial entrepreneurs. Despite the carnage, some people can't help but start companies again. And again."
Shannon Henry, "And a Happy New Economy To You!," The Washington Post, December 28, 2000
The first print use of today's phrase that I could find is from a 1991 Inc. magazine article:

"OK, once is not enough. Lots of serial entrepreneurs, who spawn one company after the next, swear it."
Anne Murphy, "Double Vision," Inc., March, 1991
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However, the author's relatively casual use of the phrase (she defines it, but she doesn't put it in quotation marks) suggests that it had been "in the air" for at least a little while before that.