Born and raised in Chicago, Meacham left to study drama at Yale University and the Neighborhood Playhouse, New York.

[1][2] She debuted on Broadway as Ensign Jane Hilton in the 1952 The Long Watch,[3] for which she received a Clarence Derwent Award, a prize for newcomers to the New York stage.

[1] She appeared in many on- and off-Broadway productions, often adaptations of plays written by Tennessee Williams, such as Suddenly Last Summer, The Gnädiges Fräulein and In the Bar of a Tokyo Hotel.

[1] For her interpretation of the role of Catherine Holly in Suddenly Last Summer (played by Elizabeth Taylor in the film version), she received an Obie Award as Best Actress.

[1][4] Other Broadway appearances included Jean Giraudoux's Ondine, Eugenia, an adaptation of Henry James's The Europeans, The Crucible and The Seagull.