Of course chess is a sport, what were you worried about? It is easy to argue chess as a mind sport, but people are often doubtful to call chess a full-fledged sport. However, the skeptics can be silenced when you flamboyantly proclaim that chess is a recognised sport of the International Olympic Committee. Whilst the IOC does approve of chess, it does not feature in the Olympics. Presumably, this is because it is too difficult to arrange – anyway, we already have a World Championship, World Cup and World Teams Olympiad! Any addition of a further world-class tournament would just be confusing.
Here is the visual evidence, from Wikipedia: