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.
Offaly Camogie Entertain Clare In Must Win Encounter
Offaly’s Ellen Regan Defies Injury As Heatwave Championship Battle Heats Up
Westmeath Ladies Looking To Reach All-Ireland Intermediate Semi-Finals
Shane Lowry Hoping For Positive Week At Travelers Championship
Offaly Golfer Aiming For Big Week At Open Championship
Alex Dunne Looking To Keep Up Momentum In Spielberg
Shane Lowry Turns Attention To Travelers Championship
Midlands Players Selected On Ireland Squad For Australian Football League Women's Clash
Midlands Golfers To Compete At European Amateur Team Championships
World Cup: Lionel Messi Makes History
All-Ireland Knockout Place Still A Possibility For Offaly Camogie
Athlone Town Play Out Draw With Wexford
Offaly Suffer Heartbreak In Tailteann Cup
It's Been A Joy To Be Involved With This Group - Mark McHugh
Lily Agg Wins First Game As Athlone Town Manager
Cork Knock Offaly Out Of Hurling Championship
Westmeath And Offaly Suffer Championship Ending Defeats
We've Constantly Improved Over The Course Of The Championship - Johnny Kelly