The game will probably be played on Saturday, February 2 (just after the transfer window closes) as it's unlikely to be chosen for TV.
The full draw is:
Morton or Gretna v Queen of the South
Falkirk or Aberdeen v Hamilton or Brechin
Airdrie Utd or Kilmarnock v Celtic
Hearts or Motherwell v Huntly or Dundee
Livingston or Cowdenbeath v Partick or Dunfermline
Hibernian v Rangers or East Stirlingshire
Cove Rangers or Ross County v St Johnstone or Raith Rovers
St Mirren v Clyde or Dundee United