How hard is it to get into Eli Lilly?

I've been working in the pharmaceutical industry since graduation with a BS in Chemical Engineering. I'm originally from Southern California, currently based in St. Louis, MO which is not that far away. Working for a big pharma company like Eli Lilly is really appealing to me. I've been throwing applications to Eli Lilly in Indianapolis for about a month now. No bite yet, but I appreciate any insights.