I've heard of claims that aphids can be born pregnant, like tribbles in ''Star Trek''.
However, doing a web search didn't provide very convincing evidence.
The Straight Dope refers to being pregnant before birth as paedogenesis. The Wikipedia article on paedogenesis has no citations on pregnancy before birth (it does, however, have a citation on male offspring eating its mother!). It also states that the term also refers to animals that get pregnant before they're fully sexually mature.
Searching for paedogenesis in pubmed only got 8 hits. (Is pubmed an appropriate tool for such a search?)
Are animals being born pregnant well-established but little discussed, or is is yet to be well-established?
(Note: I'm referring to organisms being pregnant to their own offspring, rather than accidentally being pregnant with their own siblings)