The U.S. is increasingly a destination for college students from abroad.  While it is well-known that the representation of foreign doctorate students at U.S. universities, particularly in science and engineering fields, has increased dramatically over the last three decades, the growth in the participation of undergraduate students is less well-understood.  In this paper, we trace out the notable increase in enrollment from abroad, largely as full-pay students, at colleges and universities, identifying particular increases from countries where incomes have expanded rapidly in recent decades.  We model variation over time in the foreign undergraduate enrollment in the U.S. in terms of costs, home country opportunities, and incomes.  In addition, we examine the supply-side accommodation in the U.S. to changes in demand from abroad and find that adjustments are particularly marked in those states and institutions where local demand is most likely relatively weak.