find a passage in this chapter that suggests to the reader that luck is something a pearson is born with.

Part of the nature of luck is that it can't be developed in any meaningful sense, so it makes sense to say that someone is "born" with luck insofar as we recognize that. 

Multiple instances of Bilbo’s luck in this chapter: he woke before the spider finished wrapping him up; he picked the right direction to look for the dwarves after; the spiders didn’t fully close the ring around him when he was first taunting them with song; and a spider had left hanging down a rope to the branch with the dwarves. That is quite a lot of luck in a very short space of time.