Dear NC, The answer to this questions is a definitive…sometimes.
You see, the Chimney Balloon is designed to burst and release at right around 200 degrees Fahrenheit. So if you burned a few candles and kept about a 3′ distance between the flame and the Chimney Balloon and kept your glass doors open (if you have them) then you will probably be OK to leave the Chimney Balloon in while burning the candles.
I know my wife has lit candles for up to 4 hours in our fireplace and not removed the Chimney Balloon and everything was fine. The key is to keep the wicks trimmed on the candles. If you get along yellow flame on your candle you can really get some serious heat coming from a candle that might get over 200 degrees.
So keep the candles short and away from the Chimney Balloon, keep the wicks trimmed, and keep your glass doors open and you should be fine.