This site mentions that he speaks Tamil and English, and can also speak in German & French. So he surely speaks it, not sure about the reading and writing part.
https://www.essentiallysports.com/lesser-known-facts-about-viswanathan-anand/
I have a question about Viswanathan Anand
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Does he know the language of his home state in India(Tamil Nadu), the Tamil language?
Including reading, writing and speaking?