I was just watching Chile against Australia in the World Cup, and the commentator (who seemed to be from Britain) constantly referred to the Chilean team as /tʃɪˈleɪən/. I have never heard that before, and for me it would be /ˈtʃɪlɪən/.
I then checked the Longman Pronunciation Dictionary (3rd edn), and indeed /ˈtʃɪlɪən/ is the only possibility listed for British pronunciation. However, for American pronunciation, /tʃɪˈliːən/ is given as the most common, followed by /tʃɪˈleɪən/, so the commentator was using the second pronunciation found in the USA.
I wonder if a sound change is taking place in how we are expected to say the word. When I was young, Caribbean was pronounced /ˌkærɪˈbiːən/ (with the main stress on the third syllable). But nowadays, it seems to be /kəˈrɪbɪən/ (with the stress on the second syllable). Perhaps the pronunciation of Chilean is also undergoing change.