In a Joint Parliamentary session, where both the Rajya Sabha and the Lok Sabha come together, the Speaker of the Lok Sabha is eligible to cast the deciding vote over a bill. The Speaker of the Lok Sabha is the presiding officer of the lower house of Parliament and has the authority to make decisions in case of a tie or stalemate.

The Chairman of the Rajya Sabha, option 1, is the presiding officer of the upper house and does not have the power to cast the deciding vote in a Joint Parliamentary session.

The Deputy Speaker of the Lok Sabha, option 2, is responsible for assisting the Speaker in the proceedings of the lower house but does not possess the authority to cast the deciding vote.

As for option 4, the Prime Minister, they do not hold the power to cast the deciding vote in a Joint Parliamentary session.

Therefore, the correct answer is option 3, the Speaker of the Lok Sabha.