I can't say anything about the etymology of chad but I do know that, in the United States Navy in the late 1960's, we used radio teletypes to transmit lots of messages ship to shore. In addition to clacking out a typewritten message, the machines produced a long ribbon of paper tape, about 5/8ths of an inch wide, into which was punched a pattern of holes which represented each character in the message. The tiny bits of paper dislodged from the holes fell into a little drawer which had to be emptied periodically and the stuff which came out was called "chad."

A rotten trick to play on rookies (we called them "nugs" which meant "new guys") was to tell them that a message could be completely reconstructed from the chad, thus, from time to time, we would hold "chad drills" in which the new man was assigned to empty the little drawers as fast as possible, place the confetti into a burn bag and rush it to the incinerator for secure disposal. The new guy would return from this mission, red faced and breathless, to the laughter of his shipmates.

Chad also acquired a secondary meaning of junk, trash, a thing of no value, something to be discarded.