Combine butter, sugar and cocoa powder. Stir in crumbs. Press evenly over bottom of greased 9-inch springform pan and bake at 350 for 10 minutes. Cool pan and grease sides.
Beat cream cheese until smooth. Gradually beat in sugar. Beat in eggs, one at a time. Blend in Bailey s. Pour about 1/3 mixture into a bowl and stir in melted chocolate. Pour half of plain mixture into prepared pan. Drizzle with half the chocolate mixture. Repeat layers. Make a marbled design by gently swirling batter with a knife. Bake 10 minutes at 450, then 55 minutes at 250.