It was purportedly invented at the Trader Vic's restaurant in Oakland, California in 1944. Trader Vic's rival, Don the Beachcomber, claimed to have created it in 1933 at his then-new eponymous bar (later a famous restaurant) in Hollywood. Don the Beachcomber's recipe is more complex than that of Vic and tastes quite different.
"Maita'i" is the Tahitian word for "good." The spelling of the drink, however, is two words.
The Trader Vic story of its invention is that the Trader (Victor J. Bergeron) created it one afternoon for some friends who were visiting from Tahiti. One of those friends, Carrie Guild, tasted it and cried out: "Maita'i roa ae!" (Literally "very good!", figuratively "Out of this world! The Best!") — hence the name.
The Mai Tai became such a popular cocktail in the 1950s and 1960s that virtually every restaurant, particularly tiki-themed restaurants or bars served them. The Mai Tai was also prominently featured in the popular Elvis Presley film Blue Hawaii.
Today, the Mai Tai is synonymous with Tiki culture, both of the past and present. Virtually every modern tiki gathering centers around the Mai Tai in some fashion. Contemporary tikiphiles are quite meticulous about the Mai Tai and insist that it be prepared according the traditional Trader Vic's recipe.
As of 2008, Trader Vic's Restaurant chain has begun to open small establishments called Mai Tai Bars, that primarily serve cocktails and pupus (appetizers).