Originally Posted by
Zouf
It will deteriorate the chainrings faster. If the chainrings have the same mileage as the cassette, they may not be in great condition either.
Chainrings are remarkably tolerant of worn chains within reason. I've gotten over 30,000 miles on a set of Shimano 105 chainrings and only change the chain at 5,000 or 6,000 mile intervals. Unless the chainring teeth are badly pointed or hooked, don't worry about them.
BTW, Timcuppery has a photo of a BADLY worn chainring he posts every so often and if yours doesn't look like it, you're ok.