Joining the parachute regiment with asthma.?

Hello I have been working towards a career in the RAF as a pilot for some time now and have recently discovered I am unable to due to the fact I have exercise induced asthma. I have since turned my attention to the parachute regiment. Is there any chance I would be able to join I have decent fitness level and can complete a cross country event without much trouble. I understand it wouldn't be easy but if I was to work on my fitness and endurance levels would I have a chance.