We do not automatically save a record of one to one conversations that take place via Hangouts Chat, in the same way that we wouldn't record SMS messages, face to face conversations etc.
It is possible for individuals to turn on conversation history on particular Chats though - please be mindful that if you do this the conversation is stored in Gmail and will be disclosable under data protection rules such as Freedom of Information Requests and Subject Access Requests. A conversation will display whether the history is 'on' or 'off' next to the box where you type a message.
Get the most out of Hangouts Chat and all the G Suite apps with training guides, cheat sheets, tips, customer examples, and other resources on the G Suite Learning Centre.