OK. Some background.
First, thanks for all of the replies. This has been one of the worst weeks of work in my life. I’ve had to spend almost every waking moment of my workday with this woman for the past week in a tiny conference room. I may snap over this. She is someone I will have a close working relationship with over the next year, and I just can’t take it.
This is a new job for me, and the company is European. She is European. The other man sitting in the conference room is European (from Germany). That’s why I asked. He seems not to mind at all, whereas my eyes are watering. I almost threw up yesterday and had to leave the room. Coming back was pure torture. I took a deep inhale before entering the conference room, ran to the other side and then exhaled. I spent the rest of the day with my fingers close to my nose, sniffing anything and everything to get away from the stench. She reeks every day, and she reeks morning, noon, and afternoon. She doesn’t appear overly dirty, and her hair seems to be clean. But the underarm odor is unmistakable. I’m getting sick just writing about it.
Here’s the other problem. She is in HR. I am not sure what the protocol is, but I do feel like if I speak out, she will know it was me. I am afraid this will hurt our working relationship. She is overly sensitive and has cried in my presence twice already.
I find it interesting to hear about depression as a possible link. I do not know much about her, but I do know that she lives alone, has no family or friends in the area, and as far as I can tell, no dating prospects. Still, she HAS to smell herself, doesn’t she? I can’t stand my own odor, and if I don’t shower once a day, I know I STINK.
Still, I may have an oversensitive nose. But when I skip lunch because I’m afraid I will throw it up, there has to be a solution. Perhaps next week I will approach an HR VP who may be able to steer me in the right direction without too much noise. I know how people talk, however, and I really am afraid this will be a fatal blow to our working relationship. She is very smart, but she is also very ripe.
By the way, Stink Fish Pot has nothing to do with my scent! 
Thanks for all of the advice. I’m sure I will have an update next week, as we are scheduled to spend Monday, Tuesday, and Wednesday together. On the bright side, we will not be in such a small group, so perhaps I can poll the others to see if I’m the only one who is gagging.
I don’t know. All that I DO know is that I can’t work this way much longer. I’d hate to quit over a stinky co-worker, but that’s where I am.
SFP (thinking of changing my name because of this!)