South Florida said: "Believe what you want. I have no convictions, clearly he (Chernow) thinks he's the son of Stevens, has your research been more thorough?"
Chernow certainly doesn't say he clearly believes it, just that it's a theory he finds credible. I disagree. It rests mostly on the fact that Stevens took Alexander and not James (Alex's brother) in, and the fact that Alexander and Ned were described by someone who didn't know them as looking like brothers.
Consider against that the character of James Hamilton senior, who abandoned his family when Alexander was ten. Who had been moving them around for a while, and who cut and run when he could. Does he really sound like the guy who'd be down to claim a child that wasn't his?
Adding to the recent documents unearthed that indicated Alexander may have been taken into the Stevens home as a servant (Though again, I don't count this as totally credible because a single vague document is not enough on it's own)
And the sexism Rachel (Faucett) faced after having the nerve to try and divorce her husband. Even in the show, they call her a whore. For... divorcing her husband and having children with her partner of ten years?
Those are just a few points, it's late and I don't feel like digging up all my sources and flipping through the chernow. But also consider:
Alexander Hamilton firmly believed he was James Hamilton's son. They were in contact for years and years after Hamilton established himself in america (Usually James asking for money and Ham being a doormat, but anyway). He carved the Hamilton family crest onto his powder horn. He reached out to distant Hamilton relatives in Scotland. He firmly believed he was James Hamilton's son.
James Hamilton also believed that Alex was his son. Enough to claim him (Which he didn't have to do, Rachel was not legally his wife), raise him for years, and stay in intermittent contact for the rest of his life.
the bottom line is - we can't know. Documents from that period of his life were both extremely rare and often inaccurate. It is a theory some people believe in. I don't, and furthermore I don't think it matters. Whatever Hamilton's biological parentage, he grew up as the son of James Hamilton and that's what's important.