Head over to Google+ and open the Hangouts chat sidebar – if it’s not open already; you can do this by clicking on “Hangouts” towards the top right of the page.

Now, click on the chat thread that you wish to disable chat history for, and click on the gear icon. If you’re already in a chat, you can just click on the gear icon from the chat window.

Finally, uncheck the box next to “Hangout history” to disable it and click on the “Save” button. Chat history will be disabled for that specific chat only. If you want to disable Hangout history for more threads, you will need to go to each one individually and repeat the above steps.