when should I replace the timing chain on my 2002 Honda Civic and should I have the belt tensioner replaced at the same time?
If it has a chain it doesn’t need a belt tensioner. If it has a timing belt, then yes, replacing the tensioner at the same time as the belt is a common recommendation.
I meant to say, if it has a chain it should not need to be replaced, ever, at least until the engine needs to be rebuilt.
You need to consult the Maintenance Schedule that should be sitting in your glove compartment.
If your car has a timing belt, which I believe that it does, the Maintenance Schedule will give you the recommended mileage and the recommended elapsed time interval for replacement of this item. If you have a timing chain, the Maintenance Schedule will not list any maintenance procedures for that part, as it is normally not replaced unless it begins making noise or unless you are tearing down the engine for some other major repair.
And, as was said, if you are replacing a timing belt, you should also replace the tensioner for it, as well as the water pump. Note that the water pump replacement will not be listed in the Maintenance Schedule, but is highly recommended.
There is no substitute for educating yourself about your car, and the best way to do it is to read the Owner’s Manual and the Maintenance Schedule!
Timing chains do not have an infinite life, the do “stretch” over time which affects the cam timing slightly, I like to replace mine every 200K miles, or so. I certainly wouldn’t reuse the old chain in a rebuilt engine. The chain guides also wear and eventually need to be replaced. I suspect the OP’s car has a belt not a chain, anyway.