Hibs' last Scottish Cup tie was the 5-1 humiliation by their Edinburgh rivals at Hampden, but they are a much-improved team this season and sit level on points with SPL leaders Celtic, seven places above Hearts.
The draw also set up a Highland derby with Ross County hosting SPL rivals Inverness.
The Old Firm were kept apart with Rangers drawn to face Third Division rivals Elgin City and Celtic taking on the winners of a replay between Arbroath and Inverurie Locos.
Aberdeen v Motherwell
Partick Thistle v Dunfermline Athletic
Kilmarnock v Queen of the South
Hibernian v Hearts
Airdrie United or Raith Rovers v Deveronvale
Turriff United v Albion Rovers or Morton
Livingston v Dundee
Rangers v Elgin City
Forfar Athletic or Nairn County v Ayr United
Ross County v Inverness Caledonian Thistle
Celtic v Inverurie Locoworks or Arbroath
Dumbarton v Hamilton Academical
Cowdenbeath v St Johnstone
Stranraer or Queen's Park v Dundee United
Stenhousemuir or Berwick Rangers v Falkirk
St Mirren v Brechin City or Bonnyrigg Rose
Matches to be played on the weekend of 1/2 December