Bachelor's from third world university + master's from LSE. Will I be considered for a PhD?

[finrod]

Hey everyone. 

So the title basically says it. I graduated at the top of my cohort at the national university of a small Latin American country. Now I am pursuing a master's at LSE. Things are looking good in terms of grades, prospective references, and research ideas. Maybe I even stand out a little (?!)

My area of research will probably be political theory, socio-legal studies, or something related.

I was looking, however, at the current lists of PhD students in some universities (say, Princeton or Oxbridge, that sort), and the vast majority of them seem to have obtained their undergraduate degrees at equally prestigious institutions, plus a nice master's in many cases. I could find very few people with previous degrees obtained in Latin America! Given my background, and should I earn a distinction at LSE, would I be competitive against applicants with a better institutional history?

Is it even worth trying, or should I rather be looking at some of the lower-tier universities for PhD purposes?

Thank you very much for your comments on this, and best wishes to all.