The former 'Sex And The City' actress accompanied the Oscar-winning writer to the Los Angeles premiere of his new TV series 'The Newsroom' and the happy couple couldn't keep their hands off each other.
They willingly posed for photographers with their arms around each other and later on, Aaron planted a big kiss on Kristin's lips.
Kristin, 47, looked her usual stunning self in a knee-length turquoise dress, while 50-year-old Aaron was dapper in a suit and tie.
Kristin was first linked to Aaron last month and friends say she is smitten with him after dating for six weeks.
One pal said: ''It's been going on for around six weeks. They are really happy. They have actually known each other a while through mutual friends and would sometimes bump into one another at industry events, but it has only just turned into something more.
''He is obviously really smart ... and Kristin is very intelligent, too. They have a lot to talk about.''
Both Kristin and Aaron have battled alcohol addiction in the past and have successfully stayed sober, which friends say has helped them Bond.
Aaron - whose screenplay for 'The Social Network' won an Oscar - was previously married to Julia Bingham, with whom he has a 12-year-old daughter, Roxy.
Last year, Kristin - who has never been married - adopted daughter Gemma Rose as a single parent.
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