ORIGINAL: Rodney
Wheel alignment can be a problem. Be sure to have a bit of toe-in on the gear. Exponential on the rudder also helps as it is easy to over control if you get to much rudder input. Cubs seem to have a liking for a slightly more nose heavy CG than many planes, try about with CG at about 25% chord until you get used to flying it. I strongly disagree with moving the the main gear forward as that will make landing very difficult with lots of bouncing with the resultant wing tip damage. You want the axle just ahead of the CG when the plane is in level attitude.
This is great advise. Moving the CG forward gets it closer to the mains and will make the tendency to swap ends more managable. Moving the gear forward in addition to causing the bounces also moves them farther forward of the CG making the ground loop problem worse. Remember the CG wants to be ahead of the center of drag. In the air that center is far aft of the CG due to the large tail surfaces, on the ground it is at the wheels. The farther the CG is aft of the wheels the greater the tendancy to swap ends.