Kelsea Ballerini and Chase Stokes Hold Hands in Date Night Video

Kelsea Ballerini and Chase Stokes are hanging out in her home state ... and we've got them looking cute and getting flirty on date night.

The country music singer and "Outer Banks" star went out Tuesday night in Nashville, hitting up Robert's Western World for a little bit of live music with their dinner.

We got this video of Kelsea and Chase sitting face to face at a table ... and he leans in to whisper in her ear before putting his hand on top of hers. Fair to say, things are moving along for the new couple.

Folks who were there say it was clear they were enjoying each other's company over an appetizer -- no kissing or any other heavy PDA, but they were vibing, chatting and generally getting along well.

Sounds like this could've been one stop on a night of honky-tonkin' in downtown Nashville ... because they were only at Robert's for about 30 minutes before they left.

TMZ broke the story ... Chase confirmed he and Kelsea are an item, after they kicked it at the National Championship football game at L.A.'s SoFi Stadium. He told us she's a sweet girl and they're having a good time together.