Clover ,
Chewing gum is made from rubber so to dissolve it you need a solvent.
Because rubbers are long chain molcules with high molecular weight , they are difficult to dissolve with solvents and water based products are just not in the frame.
The other approaches are to change it into a plastic by reducing the temperature , thereby embrittling the gum.
Or to make it flow by increasing the temperature by using a steam gun.
Cheers,
Doug
I see Gavin has suggested Sol.6 which is presumably a solvent based product.