chat (someone) up
1. To engage someone in lighthearted banter or casual conversation. I love chatting up tourists visiting our city, it gives you such diverse and interesting perspectives!
2. To engage in flirtatious conversation with someone, usually in pursuit of romantic or sexual purposes. I was chatting up this cute guy at the bar last night and managed to get his phone number! I hate when people chat me up in bars. I just want to have a nice time out with my friends!