It means "Thanks! Let's chat some other time again!" "またチャットしようね" can be divided into "また", "チャット","しよう"and "ね". "またmatta" means "again, some other time, another time" here. "チャットchatto" means "chat". "しようshiyou" means " let's". e.g. 開始しよう（Let's begin） "ねne" is a modal particle, which makes a sentence softer. Hope this helps:)

"Thanks! Let's chat later!"