LeAnn Rimes and Eddie Cibrian take their love to the links

LeAnn Rimes separated from Dean Sheremet in July after seven years of marriage .
Fore! Look out, because after having several secret and low-key rendezvous, LeAnn Rimes and Eddie Cibrian emerged for a very public golf date Thursday.

It’s a weekly tradition for Rimes to hit the links, and around 1 p.m. she arrived at the Valencia Country Club — shortly after her surprise partner for the afternoon. “Eddie arrived at the private country club in his Porsche a few minutes before LeAnn,” said an eyewitness. “LeAnn was beaming when she saw Eddie and the two gave each other a quick hug. Eddie was sweet and went to buy water and energy drinks from the golf store.” Good move, too: The two spent almost three hours on the golf course in 90-degree heat. “LeAnn was sans makeup and looked very happy and carefree. Between holes, LeAnn leaned back, put her feet up and sipped her energy drink while Eddie drove her around on a golf cart,” added the source. “They weren’t super affectionate, and instead more flirty in a fun and loving way.” Despite their attempts to be discreet, the eyewitness told PEOPLE, “They had lots of chemistry. They are a cute couple and they looked very happy and comfortable together.” After the golf date, which took place just one month after the news broke that Rimes, 26, separated from her husband Dean Sheremet, the couple went their separate ways.