Pete Davidson might have another body on his hands -- because he was out on a grocery store date with a mystery woman ... whom we're told appeared to be Chase Sui Wonders.

The ex-'SNL' star was out at a Whole Foods Saturday afternoon in Brooklyn, where he was definitely trying to lay low and stay incognito -- as was his lady friend next to him ... both of them wearing their hoods completely over their heads as they exchanged smiles at checkout.

Fortunately, PD recycles his fits a bit ... and we'd recognize that nifty New York jacket anywhere. It's the same one he wore at the Rangers game on Thursday ... where Chase Sui was also in attendance with her fellow "Bodies, Bodies, Bodies" cast member.

They weren't hiding then, but if this is in fact CSW -- which an eyewitness insists it was -- then they're definitely not trying to be seen together here ... which could signal they're a thing.

The cat was almost outta the bag at the hockey game ... but there was plausible deniability since their other 'BBB' costar, Rachel Sennott, tagged along -- and it could've been a 3-way friendly outing. But, if Chase is hanging with Pete solo ... well, life might imitate art after all.

If you haven't seen their movie yet, they actually play a couple onscreen ... David and Emma, who have a rocky relationship. Based on these get-togethers between them lately ... their chemistry in the real world seems to be much stronger ... with a lot less drama.

We haven't seen Pete with Emily Ratajkowski lately either -- so more evidence this might be romantic. Plus, you don't just bring anybody to WF with ya ... that's the real deal right there!