This family has been researched by others. I don't have the documentation in front of me, so I may be mis-remembering the facts slightly, but the short answer is that Raleigh Chinn I was the father of three sons by Margaret Downman (her married name), and that he acknowledged them in his will. All three later took the surname Chinn. If I remember correctly, their names were Charles, Christopher and Elijah.
I believe that Raleigh Chinn I was the legitimate father of Raleigh II, but please don't take my word for it here. Nearly every Chinn family has a son named Raleigh or Rawleigh, and I may be confusing some of them.