"Strip tease" grew out of burlesque, about 1925-1927. The name of the first person to perform this is not known. It is also not known if the first "strip tease" was an accident (recall: "wardrobe malfunction") or deliberate.
Sidewalks of America:
Folklore, Legends, Sagas, Traditions, Customs, Songs, Stories and Sayings of City Folk
edited by B. A. Botkin
Indianapolis: The Bobbs-Merrill Company, Inc.
[*From Strip Tease, The Vanished Art of Burlesque, by H. M. Alexander, pp. 14-21, 33-38. Copyright, 1938, by Knight Publishers, Inc. New York.]
I. HOW IT STARTED
She ought to be able to tell you something; she's been producing burlesque shows for the Minskys since 1930.
"What started all this?" you ask her.
"An accident at the Gotham," she replies.
"Sounds like a mystery story," you say.
"In a way it is. It may not have been an accident. It probably wasn't the Gotham, no one's sure who the girl was."
Mrs. Vivian tells you that some one in the show was singing, or dancing, or maybe she was just in the chorus when her shoulder strap broke. The audience riotously approved. THe girl liked the applause. At the next performance she broke the strap herself but not at the one after. She was in jail, the first of a long, long line.
"What year was that?" you ask.
"About 1927, I suppose."
"And that's all there was to it?"
"What more would there be? The girl went back to her show, wherever it was, and continued breaking her shoulder strap until she discovered a few snappers could be undone with less effort and more grace."
(Pg. 303 - ed.)
"It's funny about that story," grins Garns, "but I don't think there's anything in it." (...) "At stag shows, Billy Minsky didn't invent the strip. He just brought it out from the back room."
"When was that?" you ask. You'd like to get the date more or less fixed.
"About 1925. The Broadway leg shows forced him to do it."
26 June 1932, Chicago Daily Tribune, pg. F9:
In another ten years he [Billy Minsky - ed.] had made Broadway - meaning Broadway around the Times Square district - burlesque conscious. No less than three theaters -- the
Central, the Republic, and the Eltinge -- were housing entertainment having the "strip tease" as a feature.