Rajamani came to the meeting from Puliyankdiand village and was seated in the venue when he suddenly swooned around 3.30 pm, about an hour before Jayalalithaa arrived there.
He was rushed to a government hospital but was declared brought dead, police said, adding the cause of the death would be known only after post-mortem.
Jayalalithaa addressed the meeting around 4.30 pm.
Rajamani is the latest to die at Jayalalithaa's election meeting venue. Earlier, five persons had collapsed and died due to suspected heat stroke at various places, including Salem and Dharmapuri, last month.
