The seat was represented by late chief minister J Jayalalithaa.
The counting began by 8 am at Queen Mary's College here and the process is expected to be completed in 19 rounds.
As many as 200 officials drawn from both Central and State government services have been deputed for the exercise.
Tight security is in place with state and Central Armed Police Forces personnel providing multi-layered security.
The outcome of the result is crucial for all key contenders - the ruling AIADMK, rival leader T T V Dhinakaran, and the main opposition DMK.
Also Read
For the ruling regime helmed by Chief Minister K Palaniswami and his deputy O Panneerselvam, it will be seen as an acid test of whether voters prefer them after the demise of their formidable leader late Chief Minister J Jayalalithaa.
For Dhinakaran, who claims to represent the welfare legacy of Jayalalithaa, the bypoll success is a veritable springboard for his future political aspirations.
Success for an aggressive DMK is critical as it would lend credence to its campaign line that the people were fed up with the incumbent "horse-trading" regime and wanted to bring it to the seat of power for dispensing good governance.
A win in this bypoll could help it project itself as a much more redoubtable key opposition party.
While there are 18 micro observers drawn from Central government services, each of the 14 counting tables will be monitored by one of them, according to election authorities.
The entire counting process is being videographed and arrangements have been made to announce the results after conclusion of counting of each round.
The bypoll held on December 21 had seen a record 77.68 per cent voter turnout.
The ruling AIADMK got back its Two Leaves election symbol back following merger of factions led by Palaniswami and former rebel O Panneerselvam.
The 2015 R K Nagar bypoll in which Jayalalithaa was elected by a huge margin of 1.5 lakh votes for the first time in this segment had witnessed a record 75 per cent turnout.
R K Nagar, represented twice by Jayalalithaa, has an electorate of 2,28,234, comprising 1,10,903 men, 1,17,232 women and 99 transgenders.
Disclaimer: No Business Standard Journalist was involved in creation of this content