Do I have any chance with a Beautiful Rich Girl when I'm Poor?

She is a European student at Harvard and comes from a famous and very wealthy family with quite a well-known last name. My background is very average. My family is very average and ordinary and I am just a very good student. She is gorgeous and I am infatuated by her. I would love to get to know her intimately. I watch her in class every day. I really want to ask her out for dinner. She appears friendly, but I am afraid she will outright turn me down once she finds out about my background. Do I have any chance of getting serious with her?