The subject has come up regarding the candidacy of Senator Ted Cruz, who was born in Canada. Here is a short and informative article:
Note especially the last few paragraphs. I’m no lawyer, but it seems clear that the answer for eligibility for Senator Cruz is probably yes, and it will be “probably yes” until the U.S. Supreme Court accepts a case on the question. Have to wonder what the Supremes would decide. My guess is they would affirm “natural citizenship” for persons who have at least one natural U.S. citizen as a parent no matter where they were born.