Rat Racer,
Dude, don't listen to the others telling you to have a backbone. You do need a backbone, but not for the reason they say. Just deal with it brother. She's obviously a pig, but for you to bring it up spells your doom, especially as a fresh out of college guy.
Know this:
1) There are annoying people at any job you will ever have. Just understand that going in. If you're going to let that kind of thing piss you off, then you're in a for a world of hurt as your career continues. People will call you "guy" or "ace" or "dude". Some a-hole will grab that thing on the back of your shirt and say "fag tag". Some will hate you because you're thin, and they'll tell you that too thinking that it's a compliment, and they'll say things like "I bet you can eat anything you want." You just can't answer back "Yeah, because I run 90 miles a week you fat bastard!"
2) This "girl" (better get used to calling her a "woman" unless she's 17 or younger) might not be your problem directly if you criticize her, but trust me, if you do, there will be others there who have been there 5+ years who will think you are some arrogant, high maintenance pain in the ass. Promotions are recommended or handed out by these other people, and even if you don't see yourself there for long, recommendations for hire at another company come from them too. After all the education is sifted through, jobs are gotten sometimes based on how well a person gets along with others, and if you do petty stuff like telling an adult woman to close her mouth when she chews, then you aren't getting along with others. If she hasn't learned to shut her mouth when she chews by now, then she will never learn it.
I've worked with a ton of pain in the ass people. One woman interrupts all the time - even her bosses. She has little chance to advance due to that one personality flaw. One guy would just never go along with what everyone else felt was the right way to go - he was an obstructionist to the nth degree, and not in a good way either. He was ALWAYS wrong.
Don't be a putz. Buy yourself some headphones and listen to music or something if your company allows it, and for God's sake, don't look into her disgusting mouth if it bothers you.
You will be egged on by know-nothings to say something to her, but trust me, the advice I'm giving you is the right thing to do. It is the MATURE thing to do and it is the PROFESSIONAL thing to do.
Just let it SLIDE.