In full: League Cup third round draw
The draw at Hampden set up a rerun of the 1994-95 final when the Fife club famously defeated Celtic on penalties in one of the biggest Scottish football upsets of all time.
Rangers have also been drawn at home, to St Johnstone.
The tie of the round is arguably Hibs against Aberdeen at Easter Road.
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Hide AdPremiership league leaders Hearts travel to Rugby Park to take on Kilmarnock.
It will be the first time the clubs have met since Killie manager Gary Locke was sacked by the Tynecastle club following relegation in 2014.
Former Hearts players Jamie MacDonald, Jamie Hamill, Scott Robinson and Dale Carrick have since joined the Ayrshire side.
League 1 side Dunfermline Athletic caused the big shock of the second round by knocking out Dundee. Their reward is an away tie against Dundee United in the last 16.
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Hide AdChampionship newcomers Morton have a home game against Motherwell and Ross County will host Falkirk. Livingston are at home to Inverness Caledonian Thistle, finalists in 2014.
The ties are to be played on 22 and 23 September.
Scottish League Cup third round draw
Kilmarnock v Hearts
Livingston v Inverness CT
Ross County v Falkirk
Rangers v St Johnstone
Celtic v Raith Rovers
Morton v Motherwell
Dundee United v Dunfermline Athletic
Hibernian v Aberdeen