Hm...there are a TON of different pronunciations, according to Forvo:
http://www.forvo.com/word/ottilie/
The German pronunciation seems to be oh-TILL-yeah, and the French pronunciation seems to be oh-TILL-ee.
So my inclination would be to pronounce it with that syllabic pattern, but with an American accent. That's where I got oh-TILL-ee. However, there doesn't seem to be a consensus!