Alexander Chapman is currently listed as father of William Chapman (who died 1699, New London, Connecticut). I can find no proof of this (or that William Chapman came from that Chapman family). Although currently listed being born about 1626, I suspect William Chapman was born after 1629 (which would eliminate Alexander as a possible father).
Alexander is currently listed as having died in New London, Connecticut, in 1629, which is clearly wrong. There is an Alexander Chapman who died on that date in England (is it the same Alexander??) according to the two following sources (anyone have access to the second one??: Musgrave's Obituaries Prior to 1800):