CIARA kicked off her tour in Chicago on Sunday . . . and in the middle of her set, she invited a fan on-stage, and gave him a LAP-DANCE. It was actually pretty intense. Her backup dancers held his arms back, and she slithered all over him . . . even upside down. It's unclear if this stripper segment is going to be a regular feature on the tour, or if it's just a one-time thing.