Hibs will host the Jambos at Easter Road after beating Stranraer 5-3 in the last round with Hearts getting the better of Queen of the South on penalties following a 3-3 draw.
2013/14 Scottish League Cup quarter-final draw - Ties to be played 29/30 October
Inverness v Dundee United – Caledonian Stadium, Inverness
Morton v St Johnstone – Cappielow Park, Greenock
Hibernian v Heart of Midlothian – Easter Road, Edinburgh
Motherwell v Aberdeen – Fir Park, Motherwell