Sean Penn, 48, and Portman, 27, have been dating since March 17.
The pair were seen kissing for over 45 minutes at the Tower Bar in LA’s Sunset Tower Hotel reported the magazine.
Natalie Portman
A source quoted by Star magazine said the couple first became friends when they worked together in May 2008 as jury members at the Cannes Film Festival in France.
“She stimulates him in ways no other person has, mentally or professionally,” a source told Star magazine.
“There’s a lot more there with Natalie than any of the other girls Sean’s been with.”
Sean Penn’s marriage to Robyn Wright Penn reportedly ended because he started dating actress Natalie Portman, said reports on Tuesday.
It was the second time they started divorce proceedings – the first was in 2007.
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