Yes. I have two brothers who were born in Mexico while we were living there for a few years. They have dual citizenship. Not only that, but their kids can also apply for dual citizenship even though my family left Mexico before any of us was old enough to attend elementary school.
The only reason I'm not also a Mexican citizen is because I was born during my father's summer vacation from the university he was attending at the time.
so to which country to you pledge alliegence?
and the Mexican gov't has a loophole in that they do not issue birth certificates for "everyone born here is Mexican" unless they want to