Dave Grohl Smokes Cigarette at Store After Baby Mama's Identity Comes Out

Dave Grohl's got another confession to make ... he's a bit stressed -- or at least he looked it while walking around Los Angeles!

The singer-songwriter was spotted Friday afternoon ... grabbing lunch at the luxurious Chateau Marmont before heading over to the ritzy grocery store Gelson's and then CVS.

DG -- keeping a low profile by tying his hair back and throwing a baseball cap on -- was furiously puffing on a cigarette ... getting his nicotine fix.

Grohl's appearance out came less than 30 minutes after the New York Post identified Jennifer Young as the woman who Grohl had an extramarital affair with ... which led to a pregnancy.

Young confirmed her identity to the outlet ... though she wouldn't comment on their coparenting. Jennifer reportedly lives with her mother in Los Angeles, and the two women are primarily raising the child.

As you know ... Dave announced he was having a child in a September Instagram post -- and, he said he was going to work hard to rebuild trust with his wife and children.

Grohl was photographed with his wife, Jordyn Blum, earlier this month ... though the two didn't appear to be talking much in the car.