I would guess that it means premier as in, the highest in quality or degree, since it suggests that a chess club in Paris might be particularly luxurious or exclusive. I think if it were referring to the age of the club, it would say 'oldest'. Also, so far as I know, Paris didn't have the first chess club in the world, but I could be wrong about that. I'd assume the first club would be somewhere in India, nearer to where the game was invented.