In support of a second Tournament, I offer this from a game I played yesterday...
Zaphod plays a Tournament.
... getting +1 action.
... Zaphod reveals a Province.
... Zaphod discards a Province and gains a Followers on the deck.
... drawing 1 card and getting +$1.
Zaphod plays a Throne Room.
... and plays a Laboratory.
... ... drawing 2 cards and getting +1 action.
... and plays the Laboratory again.
... ... (Zaphod reshuffles.)
... ... drawing 2 cards and getting +1 action.
Zaphod plays a Tournament.
... getting +1 action.
... Zaphod reveals a Province.
... Zaphod discards a Province and gains a Trusty Steed on the deck.
... drawing 1 card and getting +$1.
I only had one Province, but the Chapel had thinned my hand to the point where I was able to discard it for a Prize, draw it again, and discard it for a second Prize. I couldn't have done it if I didn't have two Tournaments at the time.
The key to winning with Tournament is to get Provinces ASAP, and then get lucky enough to draw them with Tournaments. Early Provinces are more important than early Tournaments, because a Province in your hand can stop your opponent's Tournament dead in its tracks. That said, Chapel improves your odds of drawing Tournament with Province, so it's probably a bit more important to load up on Tournaments in this scenario.