Except they didn't.
According to an article in the Press of Atlantic City, members of a group called New York Radical Women did show up raring to burn stuff -- including, evidently, their brassieres -- but city officials talked them out of it.
Instead, the feminists dumped items like high-heeled shoes, bras, false eyelashes and issues of Ladies' Home Journal into a "Freedom Trash Can." They paraded a lamb outside Convention Hall and held up signs with such things as "Welcome to the Miss America Cattle Auction" written on them. Inside Convention Hall, demonstrators set off stink bombs during the pageant and unfurled a sign reading "WOMEN'S LIBERATION."Some people still insist they've seen photographs of women burning their bras -- and I suppose there's some slight chance they have. But it wasn't in Atlantic City, and it wasn't in 1968. Historians are pretty sure it never happened at all.
Bonus question: Was the modern bra invented by a man named Otto Titzling?
• Is Bra Burning a Myth? - Museum of Hoaxes
• 1968 Atlantic City Protest Credited with Kicking off the Feminist Movement - Press of Atlantic City
• Bra-Burning Feminists of the Sixties - NOT - About.com: Women's History