Some say that you should do this because your chainring wears to your chain, and a new chain will also try to wear itself in in it's own way, but I personally think it's way overkill.
Can you imagine replacing $1-200 (or more) worth of parts everytime you change your chain?

Maybe in extreme circumstances you will have problems like chains coming off the drivetrain because it skips a tooth or something, but I think this is one of those things that only pros worry about when/if they're trying to get the smoothest possible drivetrain for whatever reason.

Cogs/Frewheels are almost always made of hardened steel (not always, i've snapped aluminum ones that I assumed were steel) so there won't be much wear there for the most part (check anyways).

Chainrings are made of aluminium so will definitely wear when rubbing against steel. I'd say it's only an issue if your chainring is already incredibly worn after like several years of use or a couple of months of really bad maintanence (you shoudl be cleaning and lubing your drivetrain often).
I'd change the chain, then just kinda be aware of it and a taad more careful while you break in the chain. If you're not skipping around or it doesn't have too much play, you're pretty much good to go.
And like the other poster said, check for "sharktooth" (sprocket teeth worn down and thin to the poitn of being sharp).
That's the only reason I've ever had that really justified replacing a chainring.