Could I get accepted to any graduate school with an application like this?

<p>Hi,
I'm getting ready for the graduate admissions process, but I'm worried about my gpa. I'm currently holding a cummulative gpa of 3.4 or 3.5, I'm afraid that this would be much too low to be admitted to schools like NYU, Boston University, Columbia university, University of Chicago, and, dare I say it, Harvard University. However, the last two years of my undergraduate program my sessional gpa was 3.9 out of a possible 4.0 (for the first two years it was 3.1, but fell to 2.9 during my second year). In addition to the improvement, I also scored 330 out of a possible 340 on the GREs, received a number of awards, and wrote a written sample that had received nearly 90% in one of my classes. Now,do you think I'm living in a fantasy or could I actually be admitted to (at least some of these) schools?
The thing with these schools is they don't seem to have a minimum gpa (or at least for my program), they make their decision based on all materials available, not just undergraduate gpa.
Anyways, do you think I stand a chance.</p>

<p>Thank you!</p>

<p>Program: history, PhD</p>