When you chat, you have a brief, casual conversation. You might chat with your mail carrier when she delivers a package to your door.
If you're in a talkative mood, you can chat with your roommate, the bus driver, your boss, and a drugstore cashier all before lunchtime. The conversation that happens when you chat is also called a chat: "Let's sit down and have a chat sometime this week." The earliest meaning of chat was "frivolous talk," which now is more likely to be called chatter or chitchat.