The questions says it all. Does a 2010 VW Jetta S (2.5 L gasoline engine) have a timing belt or chain? Please reference where you got this information.
For future reference, indication of that could be found in owner’s manual. Chains usually do not require maintenance, whereas belt replacement would be noted on in maintenance schedule somewhere around 150-200k km (100-125k miles).
It's a chain. It should be the same as this 2008 2.5L L5 VW engine ... #18: