I am sorry about your hen. No breathing heavy is not normal but is not always life threatening. Is she over heated from the weather? Was she scared by something and is now stressed? Feel her feet compared to the other hens feet. Are her feet the same temp as the others? What consistency is her poop? When was the last time she laid an egg? Is there anything else she is doing differently other than this breathing?
Check her over for these things and anything else you can find about her. If all she is doing is breathing heavy with no other symptoms, it may pass. If she develops something else as a symptom, then maybe we can get down to the bottom of this. Keep us posted!
Hello and Welcome To BYC! TwoCrows gave you some good suggestions. If the hen is new and it is the first day she has been outside, she may just be stressed. Be sure they have plenty of water available. You might also want to double check the temperature in your coop if it has not been set up for summer (all the vents etc open).
She may be inching towards heat illness. If she is outside maybe you can wet down the ground for her so she will feel cooler. Do you have natural shade for the flock? Maybe you can run a fan in the coop to circulate the air. Moving air always feels cooler. Make sure she has plenty of cool, fresh water. If you have anything like watermelon - chickens love that and it gets more fluid inside them.