No question. Randolph was a good little boxer, with an excellent jab, and he came off the deck to outjab and TKO the much taller Ricardo Cardona in 15. (Inside a 14 foot ring!) But Jeff Chandler is a true HOFer, and as great an amateur as Leo was, he wasn't really in Jeff's league as a pro. (They both deserve acclaim for walking away from boxing when they did, and became champions at the perfect time for American boxers at that weight to reach the top. Also noteworthy, because they may have been the only two champions in boxing at the time with cornerwomen.)
Jeff Chandler would win. Leo Randolph was an incredible talent who won a gold medal in Montreal at only 17. But he had other interests besides boxing. He didn't even have interest in turning pro, he wanted to be a truck driver. He had to have his arm twisted and be convinced to fight pro. He did win a title, and after he lost it in his first defense, he retired for good at 22. Could have achieved the things Chandler did as a pro, but wanted to do other things in his life. Chandler on the other hand was a hungry, dominant champion who ended up in the IBHOF. This is why I pick him in this one.