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Things are heating up between the 50-year-old Oscar winner and the recently divorced 26-year-old starlet!

After being spotted playing footsie during a lunch earlier this week, Sean and Scarlett had a romantic dinner date at LA's Chateau Marmont, where the couple were locked in an "intimate" conversation at the famed Hollywood hotel.

The seemingly strange duo apparently hooked up back in January, when Scarlett was shooting We Bought A Zoo with Matt Damon.

Penn is also reportedly planning on bringing his new ladylove with him on his next trip to Haiti ... along with Charlie Sheen! That should be quite a threesome!

Sean isn't the only much-older man Johansson has allegedly hooked up with in the past...