In-meeting chat can be saved manually or automatically.
Auto-save chat will automatically save your in-meeting chat locally on your computer. You can also manually save your chat when you start local or cloud recording.
Manually Save Chat
When in meeting, click on Chat > Save Chat or Record (Host or assigned by host)
To automatically save the in-meeting chat of a meeting go to Profile Settings and enable auto saving in-meeting chats under meeting options.
Chat Save Location
The meetings chat will be stored in the location of defaulted as the recording path, which can be found by opening the Zoom application selecting Settings
Then selecting "Recording" to open the location where the chat is saved.