The insertion of the first -o- is unnecessary in priciple, since -o- is intended to be placed before consonant sounds. According to this line of thinking, the correct form would be paleanthropology. However, other dictionaries seem to prefer paleoanthropology and it is 200 times more frequently used on the Internet than "paleanthropology".
From paleo- +"Ž anthropo- +"Ž -logy.
English Wiktionary. Available under CC-BY-SA license.