The messages of your Gmail, iGoogle, Google Talk, and downloaded client chats are stored in your Gmail account so you can easily search for them later.
To access your chat history, click the Chats label in your Gmail account. A list of chats will appear, similar to the way conversations are listed in your inbox. You can label, star, and trash chats just like Gmail messages.
When you search in Gmail, matching chat conversations will show up along with matching email conversations. All chats are labeled Chats and are marked with the chat icon () so you can easily distinguish them from emails.
On an individual basis, you can turn off which conversations are saved by clicking More at the top of a chat window, and selecting Go off the record. Learn more about going off the record.