No Top 10 School from my HS - What are my chances?

My guidance counselor recently told me no one from my high school's ever gone to an Ivy, MIT, Stanford, Caltech, etc. Each year, however, it seems like there are definitely qualified kids.

Our high school was built around 2004. For the last 3 years, the top 10 students in the school have all been non-URMs [non-underrepresented minorities] and non-legacies. Could this be the reason, or is the problem with the school itself?

It's entirely possible that part (if not most) of the reason no one from your high school's been admitted is that your school just hasn't been around long enough (or isn't large enough) for a student to be admitted to a top 10 school. This isn't necessarily because schools like MIT or Caltech would be prejudiced against a newer high school - it's due to the math of admissions.

Let's say that your high school graduating class has an average 150 students, and that the top 10% of them applied to Stanford every year for the past 9 years (assuming the first senior class graduated in 2008 and would've been applying to college in winter 2007-2008). That's just 135 applicants in total (15 applicants a year x 9 years). When you consider that Stanford has been getting 25K+ applications a year since 2008 (and got 42K+ applications last year) and only admits about 2000-2200 students a year (with a 5.1% admissions rate), it's not at all surprising that no one from your high school has been admitted yet.

There are of course other factors that might be at play - does your high school offer AP or IB classes? Are there extracurricular and volunteer opportunities? Does the school value students whose parents attended (and regularly contribute money)? - but the most likely explanation is that your high school is new enough that there just haven't been enough students who applied to top 10 colleges yet to be admitted.