No. The constitution has no requirement that your parents be American citizens.

Quote Originally Posted by Article 2, Section 1
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
You wouldn't even have to be born in the US if your parents were US citizens. For example, you're born on a military base in another country. You would still be a natural born citizen.