He shares the second spot with four other players, including World No. 1 Magnus Carlsen of Norway, each sitting pretty on two points.
World No. 14 Pavel Eljanov of Ukraine, with two-and-a-half points, is the current leader in this elite field.
Harikrishna, ranked No. 11 with an ELO of 2770, has notched up one victory against Indian counterpart Adhiban Baskaran and two draws against World No. 7 Levon Aronian of Armenia and Eljanov.
"I am satisfied with the way I am playing," said Harikrishna after his draw against Eljanov with black late last night. "But there is a long way to go still. I have 10 more games to play.
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The Indian will next take on Sergey Karjakin of Russia with white.
Harikrishna scored his first victory on Sunday night by outsmarting Adhiban in a long drawn out game. They were locked in the Archangelysk Variation for close to four hours until Harikrishna lured him into a trap in the endgame.
Tata Steel Chess is an annual tournament in this northern town of The Netherlands, popularly known as the Wimbledon of chess.