How can I trace my '66 Barracuda's history?

The Chysler Historical Society will know who first sold the car but you'll have to do the research after that. Try to contact the dealer (if they are still in business) and see if they can find out who they sold the car too. Also work backwards to the party you bought the car from. Maybe they will remember who THEY bought the car from. I'm in the same boat but my original dealer is no longer in business and I bought the car at an auction so I don't have any info at all!