The play, which was awarded five stars by the majority of critics, explores the story behind the photograph of The Tank Man during the events of Tiananmen Square in 1989.
It opened at the Almeida theatre in Islington last year, before transferring to the Harold Pinter Theatre in the West End.
Accepting her award, playwright Kirkwood said: “I’ve got an enormous debt of gratitude to everyone at the Almeida theatre, Sonia Friedman... and my family.
Olivier Awards 2014 red carpet round-up
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“It’s important I accept this on behalf of the whole Chimerica company. Producing this play was a huge collaborative effort and I was lucky enough to work with cast and crew who were ridiculously talented.
“Most of all I’d like to share this with Lyndsey Turner…without who the play would have been a much poorer version of itself.”
Turner won Best Director for Chimerica earlier in the evening.
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