Changing your chat history settings
You can adjust your chat history settings in Gmail at any time.
In Google Chat, you can turn individual chats off the record, but you cannot turn chat history off for all of your chats.
Keep in mind that if you've disabled chat history saving, people you chat with may still choose to save chat histories in their Gmail settings. If you would prefer that someone you're talking to doesn't save your chat, you can take the conversation off the record. If you're talking to someone who is connected to the network with a desktop chat client, it's possible that his or her software is keeping a separate copy of the chat history.
Learn more about chat history.