FIRST PHOTOS - Rihanna Goes On Dinner Date With Chris Martin

Rihanna had a most unlikely dinner date last night ... with Gwyneth Paltrow's estranged hubby, Chris Martin!

The consciously-uncoupled Coldplay frontman and the sexy pop star arrived, separately, around 9pm and stayed for 2 hours! And catch this ... X17 can report exclusively, that Gwyneth had just headed to LAX for a flight to London before Chris jumped in his Jeep, headed for dinner with Rihanna at her favorite spot, Giorgio Baldi in Santa Monica.

Our photographer tells us the two were quite cozy during dinner: "They were leaning in to each other, laughing and being flirty. Rihanna kept pushing her hair out of her face and Chris appeared to be almost whispering in her ear."

The pair had a corner table to the Italian hotspot -- Rihanna's a regular at the restaurant. She toned down her usual over-the-top fashion and opted for a black sweater with ruffled sleeves and black pants with heels. Chris wore a tee-shirt and jeans.

Our shooter commented, "They looked cute together - maybe they're working on a new project; maybe they're trying to make certain people [Chris Martin and Gwyneth Paltrow] jealous or maybe they're actually dating. I was surprised to see them together!"

Chris and Rihanna have collaborated before on the track "Princess of China," in 2012, for Coldplay's fifth studio album Mylo Xyloto. They performed the single that year at the Grammy's. Click through to see that music video -- and check out our video from last night ...