4 (3.5?) turns with help from your opponent:
T1: Opponent buys Bishop.
T1: Buy Doctor, overpay $3, trash Hovel, Necropolis, Copper.
T2: Opponent buys Bishop.
T2: D, OvE, CCC, trash 3 Copper, buy Chapel. Draw OvE.
T3: Opponent plays Bishop, you trash OvE, drawing your last card in hand.
T3: Trash everything with Chapel. Draw Chapel.
T4: Opponent plays Bishop, you trash Chapel.