American law originates from British Common Law. Specifically Common Law before we split from them. 1776 and all that. It's where the 2nd Amendment comes from and a right to defend yourself. But after 1776, our jurisprudence system was evolving along its own path.
Britain didn't overturn trial by combat until after we declared independence. No American court has really addressed it. Ergo, trial by combat may still be legitimate under U.S. Law.
If so, court TV could become a lot more interesting.
Link | Photo by Flickr user Patch Heart Photography used under Creative Commons license
Previously: Kentucky State Officials Must Swear an Oath Against Dueling