Hunt was born in Morristown, New Jersey, and raised in Westport, Connecticut. She is one of the two daughters of Raymond Davy Hunter, vice president of Harper Fuel Oil on Long Island, and Elsie Doying Hunter, a piano teacher who taught at the Westport School of Music and accompanied the Saugatuck Congregational Church choir. Hunt attended the Interlochen Arts Academy and the Goodman School of Drama in Chicago (now part of DePaul University).
Hunt's film debut in 1980 was in Robert Altman's musical comedy Popeye. Two years later, she co-starred as Billy Kwan in The Year of Living Dangerously, Peter Weir's film adaptation of the novel of the same name. For her role as the male Chinese-Australian photographer Billy Kwan, Hunt won the Academy Award for Best Supporting Actress in 1983, becoming the first person to win an Oscar for playing a character of the opposite sex. In addition, the character was Asian and had the condition of dwarfism. In her screen test, Hunt wore a hairpiece, a fake moustache, and "paste-on pieces above her eyes to [appear] Oriental". To accomplish the role during production, Hunt shortened "her hair and dye[d] it black[,] wore padding around her waist, shaved her eyebrows, and carried something in her shirt pocket." In her 1986 interview with the Bomb magazine, Hunt remarked that Billy Kwan "is supra-personal [with] layers of sexual ambiguity[.]"
Hunt also played a nurse in She-Devil (1989) and the austere school principal opposite Arnold Schwarzenegger in Kindergarten Cop in 1990. Hunt played the assassin Ilsa Grunt in If Looks Could Kill (1991) opposite Richard Grieco and Roger Rees.
Also a well-known stage actress, Hunt has received two Obie Awards and a Tony Award nomination for her theatre work. She created the role of Aunt Dan in Wallace Shawn's play Aunt Dan and Lemon. She portrayed Sister Aloysius in the Pasadena Playhouse production of John Patrick Shanley's play Doubt. She was praised for her performance as the title character in Bertolt Brecht's Mother Courage and Her Children. Hunt also appeared as Pope Joan in Caryl Churchill's Top Girls when London's Royal Court Theatre's production was staged at the Public Theater in New York. In an interview with writer Craig Gholson and actor Vincent Caristi, Hunt discussed her experience acting in theatre, "Acting onstage is like an explosion each night. And what comes in at you all the time as you are trying to . . . create something which is a tremendous act of organization and concentration.".
TelevisionHer television appearances include recurring roles as Judge Zoey Hiller on David E. Kelley's series The Practice and as Dr. Claire Bryson on Without a Trace. She has narrated several installments of The American Experience on PBS. Since 2009, she has co-starred as Operations Manager Henrietta "Hetty" Lange, on the CBS show NCIS: Los Angeles with Chris O'Donnell, LL Cool J, Daniela Ruah, Eric Christian Olsen, and Barrett Foa.