It's so hard to tell a person, "yes, you have a chance, apply," or "no, you have no chance." So much depends on how well your research interests match a department, how many PhD students they can fund that year...factors no one else has any control over. Only the admissions committee can really tell you if you have a chance and, sadly, none of us are the admissions committees (if only we were!) If this is what you want to do with your life, then apply, because the worst that happens is that you lose your application fees. It sounds like you're being realistic and planning for back-up options, so as long as you have those, go for what you want. You never know what "reach" school might actually think you're a perfect fit for one of their faculty members.
lavieenrose reacted to stizz in 2014 Applicant Profiles and Admissions Results