You will have to find an access to his book. I'm sure he cites his source in there somewhere.
I don't think he is making it up.
Then where did you get it?
OK so I'm home and I looked up the quote in my copy of Foote's book. Two things I noticed. One, in Foote's book it's not one quote. It's two separate quotes, probably from two separate occasions and two separate audiences. And two, Foote does not source any of his quotes. We don't know who Chase was addressing, when they were supposedly made, nothing. Foote could have made them up and we wouldn't have a clue. Finally, in my book the quotes were on page 1035.
So I have no idea what neo-confederate tribute site you got the quote from but they obviously doctored it to make it sound like one long quote. And without any source, either from Foote or your website, we have no idea of context. So as far as supporting evidence goes it's up to your usual standards.