Queen of the South's reward for knocking out last season's winners St Mirren is a tie with another Scottish Premiership club, when they play Hearts at Tynecastle.
Hibernian were the first team to come out of the drum in the draw at Easter Road, and they will host Stranraer, while Greenock Morton face an away tie with Celtic.
Scottish League Cup third round draw
Hibernian v Stranraer
Dundee v Inverness CT
Celtic v Greenock Morton
Livingston v Motherwell
Hearts v Queen of the South
Falkirk v Aberdeen
Dundee Utd v Partick Thistle
Hamilton v St Johnstone
Ties will be played on Tuesday 24 and Wednesday 25 September.