Were any U.S. Presidents born outside of the United States?

Technically, yes. Some were born before the USA existed!

8 presidents were born in what is now, but at the time was not, the United States. They are Washington, Adams, Jefferson, Madison, Monroe, Quincy Adams, Jackson and Harrison.

http://www.heptune.com/preslist.html#birthplaces

No. US law prohibits anyone who was born outside the US from serving as President. The above mentioned presidents were all born in what had been part of the US since the US constitution was ratified.
https://en.wikipedia.org/wiki/President_of_the_United_States


The first US President born outside what was ever among the original 13 British Colonies was Ulysses Grant (who was born in Ohio.) https://en.wikipedia.org/wiki/Lists_of_Presidents_of_the_United_States_by_place_of_birth

The first presidential candidate who was born outside the US was John McCane, who was born in the US-owned base around the Panama Canal. Because his place of birth was at the time considered to be US soil, he could have served as President had he won the election.

The official White House site is mum on the question, but some people think Chester Alan Arthur was actually born in Canada rather than Vermont. Nobody knows for sure--all who may have are long gone. One far-fetched story even has him born in Ireland and immigrating at the age of fourteen. The official version is that he was born in Fairfield, VT.

http://www.whitehouse.gov/about/presidents/ChesterArthur
https://en.wikipedia.org/wiki/Chester_A._Arthur#Early_life_and_education

Chester A. Arthur was born on October 5, 1829. Although his parents gave his birthplace Fairfield, Vermont, it is likely that he was actually born in Canada where they resided.

Chester Alan Arthur's birthplace is an interesting question.

Democrats claimed that Arthur, a Republican, wasn't born in Vermont as he maintained, but in Canada, which according to the Constitution made him ineligible for the Oval Office.

The charge was never proven, but even today there are those who say it's true.

http://www.cbsnews.com/news/the-original-birther-controversy/

It's interesting to note that the Wikipedia entry for him is entirely dismissive of the claims and controversy, seeming to indicate that the consensus is that he was born in Vermont.

https://en.wikipedia.org/wiki/Chester_A._Arthur