Printing chats directly from Teams is not possible at this time. However, try this workaround using Teams for the web.
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Log in to Teams for the web.
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Go to the chat or channel you want to print.
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In the browser, press Ctrl+P or go to Settings (...) or customize (⋮) in the upper right and select Print.
If the Portrait view cuts off the page, change to Landscape. You can only print one page at a time.