I'm a PhD student in CS at Caltech. The single biggest factor that determines whether you will get in is whether a well-known researcher writes a strong recomme

I'm a PhD student in CS at Caltech. The single biggest factor that determines whether you will get in is whether a well-known researcher writes a strong recommendation for you. I expect that it will be difficult to make the case to accept someone from a virtually unknown program like the University of Chile when there are so many qualified applicants from top American schools. Just to be clear, I'm not saying you are unqualified, only that you will have to compete with "safer bets" who look stronger on paper.