November 30, 2014 12:31 PM EST

Along with Arthur Miller’s Death of a Salesman, Eugene O’Neill’s Long Day’s Journey Into Night and a few other notable modern works, Tennessee Williams’ 1947 masterpiece, A Streetcar Named Desire, helped shape the look and feel of American drama for decades to come. But nothing that occurred during the play’s original Broadway run eclipsed the emergence of a young Marlon Brando as a major creative force and a star to be reckoned with. Here, on the anniversary of the play’s Dec. 3, 1947, Broadway premiere, LIFE.com presents photos — some of which never ran in LIFE — made during rehearsals by photographer Eliot Elisofon.

Directed by Elia Kazan and starring Brando, Jessica Tandy, Kim Hunter and Karl Malden, the 1947 production remains a touchstone in American drama, winning both the Pulitzer Prize and the New York Drama Critics’ Circle award for the year’s best play, as well as a Best Actress Tony for Tandy for her seminal performance as the unstable, alcoholic, melodramatic Southern belle, Blanche DuBois. Despite all the accolades it earned, however, the 24-year Brando’s galvanizing turn as Stanley Kowalski — in both the play and in Kazan’s 1951 film adaptation — was what really seared the production into the pop-culture consciousness.

Gritty, sensual, violent and bleak, Williams’ great play remains one of a handful of utterly indispensable 20th-century American dramatic works, while the sensual ferocity of Brando’s Stanley can still shock, seven decades after he first unleashed the character on a rapt theatergoing public.

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