In a letter to Modi, she referred to a Central team's visit to Tamil Nadu in April last year for inspecting five suitable locations for an AIIMS Hospital.
"However, so far the final decision of where the AIIMS in Tamil Nadu would be set up is yet to be communicated (to her government)", she said.
"I request you to expedite the announcement of location of the AIIMS in Tamil Nadu and to ensure that the construction and establishment of AIIMS is initiated without any further delay", she said.
"In response, in the Union Budget 2015-16, the establishment of an AIIMS in Tamil Nadu was announced."
She had also indicated then that the state had already identified the required land in Thanjavur, Kancheepuram, Pudukottai, Erode and Madurai districts.
The Chief Minister said the "prestigious project will provide State-of-the-art medical facilities and services" to the people of Tamil Nadu and requested steps for expediting the project.