H.W.
This is pretty normal 3 year old behavior. They are transitioning from needing a nap to no longer needing a nap. Instead of putting him down for a nap, put him down for a quite time. Put him in his bed, read him a book, etc... and then give him a few books to look at. Let him know that he doesn't have to go to sleep, but he does have to stay in his bed for 30 minutes (probably the max time I would do). I would then give him a little treat for either staying in bed or sleeping. I know that nap time gives you a break, but I wouldn't force it.