Step 1: Identify the event.
The Aranmula Boat Race is considered the oldest river boat race in Kerala and is held as part of the Onam festival celebrations at Aranmula, associated with the Aranmula Parthasarathy Temple.
Step 2: Identify the river.
The race is conducted on the Pamba River, which flows through Aranmula in Pathanamthitta district of Kerala.
Step 3: Rule out other rivers.
Periyar flows through Ernakulam, Chaliyar through Malappuram, and Bharathapuzha through Palakkad and Thrissur, none of which are associated with this race.
\[ \boxed{\text{Pamba}} \]