If I delete a user will this also delete the chats answered by that user?!

No. Deleting the user will not delete the chats (metadata or transcript if saved) answered by that user.  Their chats, including their username as the operator, will continue to be visible and searchable in the Chat History area.  And their chats will continue to be counted within the various built-in Reports such as Chats Per Queue, Chats Per Hour, etc...

The only caveat is the Chats Per Operator report.  A deleted user will no longer be reflected in this particular report.

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