Final answer:
The final approving authority for the 'remain in place' chit would be the President, who has the power to sign a bill into law or veto it.
Step-by-step explanation:
The final approving authority, by signature, for the 'remain in place' chit would vary depending on the specific context. However, based on the provided information, it seems to be related to the legislative process and the President's role in signing bills into law. In the United States, the final approving authority would be the President, who has the power to sign a bill into law or veto it.