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The Million Dollar Baby star - favourite with the bookies - beat off competition from Annette Bening (Being Julia), Catalina Sandino Moreno (Maria Full of Grace), Imelda Staunton (Vera Drake) and Kate Winslet (Eternal Sunshine of the Spotless Mind).
Collecting her award, Swank said: "I don't know what I did in this life to deserve all this. I'm just a girl from a trailer park who had a dream - I never thought this would happen, let alone be nominated and .. a working actor, for that matter, and now this.
"I thank the academy, to whom I'm eternally grateful for this great honour. I would also like to acknowledge my fellow nominees - Annette, Imelda, Kate and Catalina - your work inspires me beyond words."
After a long list of credits, she thanked Clint Eastwood, the film's director. "Thankyou for allowing me to go on this journey with you. Thankyou for believing in me."
