We have never had a filly win the triple crown but interestingly enough filly's do have their own version of the Triple Crown known as the Triple Tiara. Like the Triple crown it is open to 3yrs olds but no colts are allowed to run. It consists of the Acorn stakes (belmont park 1 mile), the Coaching Club American Oaks (saratoga 1 1/8 mile) and the Alabama Stakes (saratoga 1 1/4 mile). At one point it also included the Mother Goose Stakes but as part of the restructuring it was added and removed several times.
there are only 8 winners of the triple tiara and there has been some debate over whether or not it is a fair race set as they are all run in New York and so heavily favor fillys who regularly race in the northeast.
the 8 winners are Dark Mirage (1968), Shuvee (1969), Chris Evert (1974), Ruffian (1975), Davona Dale (1979), Mom's Command (1985), Open Mind (1989), Sky Beauty (1993). Although it should be noted that Wistful (1949) and Real Delight (1952) could be considered winners as they both swept the (then) current largest races for filly's (Kentucky Oaks, Pimlico Oaks [also know as the Black Eyed Susan oaks], and Coaching Club American Oaks) before the 3 races where recognized as a trilogy, much the same as Sir Barton (1919) is the first winner of the Triple Crown although it was't a recognized racing set until Galant Fox (1930) repeated his feat.
The Triple Tiara was officially named in 2003 I believe and has carried and additional bonus for winning all three races of up to $50,000 but for whatever reason it has received little in the way of public funding or recognition.