I once opened Mint/Chapel when I was new to the interface (misreading Mint for Mine). Not realizing what was going on I even kept trashing Estates and coppers with chapel until I drew less than 5 Cards.
Once I realized that this was not a Mine, but a Mint, I bought some Coppers, then Silvers and a Salvager to win the game.
I think Chapel/Mint is possibly not as bad as it seems.