You don't say specifically where the gum is stuck, and I suppose it depends on how stuck it is.Josepi said:
Wait on the pneumatic degreaser.
I would start with vegetable or olive oil.
If that didn't work, I would next try WD-40.
And if that didn't work, I would carefully try Goof Off. It's a pretty strong solvent, but if you're careful, you should be OK.
If none of those work, go to your local auto parts store and check their finish section. They have all kinds of stuff that gently removes all kinds of other stuff without harming the paint (assuming the gum is stuck to your frame).