Step 1: Recall constitutional provisions on joint sittings.
Article 108 of the Indian Constitution provides for a joint sitting of both Houses of Parliament (Lok Sabha and Rajya Sabha) to resolve deadlocks on ordinary bills.
Step 2: Identify the presiding officer.
As per Article 118(4), the Speaker of the Lok Sabha presides over a joint sitting of Parliament. In the Speaker's absence, the Deputy Speaker of Lok Sabha takes over.
Step 3: Rule out other options.
The President, Vice President, and Chief Justice do not preside over joint sittings.
\[ \boxed{\text{the Speaker of Lok Sabha}} \]