Aha, confirmed:
"It was common knowledge throughout the court that Leia was adopted into the Royal Family. What wasn't common knowledge was that Leia was born to Anakin Skywalker, a Jedi pupil who succumbed to the dark side and became Darth Vader. She was one of a set of twins, born in secrecy and protected from Vader and the Emperor. The Jedi hero and general, Obi-Wan Kenobi, saw to it that Leia was secretly transported to the planet Alderaan, where she was to be raised by Kenobi's friend Bail Organa. The boy, Luke, was taken to the distant world of Tatooine. Leia has few memories of her true mother, Padmé Amidala. All that Leia can recall is that she was beautiful, but sad. "
From http://www.starwars.com/databank/character/leiaorganasolo/
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