There's no one-click way to move a chat discussion back to the post where it originally came from (like there is to move a comment discussion to chat).
If the information in chat is valuable, the best thing to do is to edit the answer to include that information, making sure that you give proper attribution, i.e. user name and a link to their chat message (there's a dropdown menu on the left of each message with a permalink option). Valuable information certainly should not remain in comments; from the help page for the comment privilege:
When shouldn't I comment?
Comments are not recommended for any of the following:
some points elided
- Secondary discussion or debating a controversial point; please use chat instead;
The chat room for this discussion will eventually be frozen (meaning no new messages can be added) if it remains inactive for long enough, but it won't be automatically deleted. (Moderators have the ability to delete chat rooms, but in my—admittedly limited—experience, that ability is only used for rooms created for off-topic discussion.)