I would say:

"I must not have been clear when I told you earlier how much the gum popping is bothering me. I'm sure you're not doing it on purpose, but I am having a hard time concentrating with the gum popping going on. Would you please try not to pop the gum?"

Then, the next time, "I can hear your gum. Would you please stop?"

Then, the next time, "Gum. Please?"

After that, I would be sure she was doing it on purpose and I would have to have another talk with her, and then let her know I'd have to go to the boss.

Is she talking on the phone while she's doing this? More reason to go to your boss.

Karen