Is it normal to have a quick chest pain when sneezing?

Not serious: A momentary and occasional chest pain during the rapid release of air, diaphragm release, intercostal muscle movement, soft-tissue stretch, and pleural gliding during a hard sneeze isn't unusual or serious. If you have persistent pain with deep breath or cough, you may have pleurisy and should be checked.

Yes: If the pain is brief, only associated with sneezing and no other symptoms are present then i wouldn't categorize this as abnormal, especially if you're sneezing because of an upper respiratory infection that is also causing some inflammation and congestion in the chest.