From Ayn Rand Answers:

Questioner: "What is your attitude towards immigration? Doesn't open immigration have a negative effect on a country's standard of living?"

Ayn Rand: "You don't know my conception of self-interest. No one has the right to pursue his self-interest by law or by force, which is what you're suggesting. You want to forbid immigration on the grounds that it lowers your standard of living - which isn't true, though if it were true you'd still have no right to close the borders. You're not entitled to any 'self-interest' that injures others, especially when you can't prove that open immigration affects your self-interest. You can't claim that anything others may do - for example, simply through competition - is against your self-interest. But above all, aren't you dropping a personal context? How could I advocate restricting immigration when I wouldn't be alive today if our borders had been closed?" (Ford Hall Forum, 1973)