To talk to (someone) in a friendly, open, or casual manner, sometimes also in a charming or affected manner, usually to curry favor, and sometimes flirtatiously with the intention of establishing a romantic or sexual encounter or relationship with that person
talk to someone with the aim of persuading him talk or behave amorously, without serious intentions; "The guys always try to chat up the new secretaries"; "My husband never flirts with other women
If you chat someone up, usually someone you do not know very well, you talk to them in a friendly way because you are sexually attracted to them. He'd spent most of that evening chatting up one of my friends She was chatting one of the guys up