Gmail by default saves all the chat history of all the chats you do via Google talk interface or through the Gmail, so when ever you chat with some one the chat history gets saved automatically under chats section in Gmail on both the accounts.
In order to stop this chat history from getting saved in these accounts, you can follow the simple tips below with which you can stop Gmail to save the chat history for a particular chatting session with some one.
If you are chatting with some one via Gmail chat then in to stop recording Gmail chat, you will need to select the option to go off the record as shown in the image below.
In case of if you are using gtalk, then again you will need to select the option to go off the record as shown in the image below.
Once you selected the to chat with a person off the record these chats messages with that person will not get saved in neither in your Gmail nor in the Gmail account of that person you are chatting with. If you don’t want to save any chat history for all the chats you do on Gmail, then you would need to login to Gmail – go to settings >> chats and select the option which says Never save chat history as shown in the image below.
Hope you find this easy to follow.