"Play chess" is correct. In your mind you can imagine the full form "Play the game of chess" which people nearly always shorten to "play chess". Similarly "play football", and other sports. You say "play the cello" or "play the piano" even when you're not talking about a specific piano. Here the article "the" is referring to the species of instrument and not that particular piano in your living room. You can think of "I play the piano" as being short for "I play the 'piano' family of instruments."

Hi Carter, The word "chess" is a proper noun. Therefore, there is no necessity for "the" which is a determiner. Hope this help. Cheers, Lance

Ask what the expression "wag the dog" means :)

Play chess