Athlone's conquerors drawn against league champions for round two.
The team that knocked Athlone Town out of the FAI Cup are in the only all-Premier Division clash of the second round.
Drogheda United will face league leaders Shamrock Rovers.
Waterford, who knocked out holders St Patrick's Athletic are away to Malahide United.
Last year's runners up Bohemians have been handed an away tie against non-league Lucan United in this afternoon's draw.
Of the other top-flight clubs left; Shelbourne are away to Bonagee United, Derry will entertain Cork City, UCD go west to Galway United and Dundalk play Wexford away.
The fourth non-league side left, Maynooth University Town, host Treaty United - and all ties will be played on the last weekend of this month.