The draw has been made for the Third Round of the FA Cup.
Gillingham reached the same stage last season before being knocked out by then-Premier League club Leicester at Priestfield.
It was still a great day for the club, though, as it marked the introduction to their fans of new owners, Brad and Shannon Galinson.
The Gills, 2-0 winners over Charlton on Saturday, have been handed another tie against Premier League opponents with Sheffield United visiting Priestfield this time around.
Maidstone are in the Third Round for the first time since the club reformed in 1992 following the demise of the Football League side.
The Stones, 2-1 winners over League 2 Barrow on Saturday, were handed a home tie against Stevenage or Port Vale – the two League 1 sides drew their Second Round clash 1-1 on Saturday.
Maidstone beat Stevenage in the FA Cup First round in the 2014/15 season, 2-1 in a replay at the Gallagher thanks to a Frannie Collin brace after a goalless draw away from home.
Ramsgate’s televised Second Round trip to AFC Wimbledon on Monday night means they were also in the draw. The winners know they will be at home to Championship outfit Ipswich Town.
Third Round ties are due to be played across the weekend of January 6 and 7 with winning teams banking £105,000 in prize money.
FA Cup Third Round draw (January 6-7):
Luton Town v Bolton Wanderers
Shrewsbury Town v Wrexham or Yeovil Town
Arsenal v Liverpool
Stoke City v Brighton & Hove Albion
Norwich City v Crewe Alexandra or Bristol Rovers
West Ham United v Bristol City
Tottenham Hotspur v Burnley
Fulham v Rotherham United
West Bromwich Albion v Aldershot Town or Stockport County
Southampton v Alfreton Town or Walsall
AFC Wimbledon or Ramsgate v Ipswich Town
Peterborough United v Leeds United
Millwall v Leicester City
Watford v Chesterfield or Leyton Orient
Sunderland v Newcastle United
Sheffield Wednesday v Cardiff City
Crystal Palace v Everton
Middlesbrough v Aston Villa
Nottingham Forest v Blackpool or Forest Green Rovers
Wigan Athletic v Manchester United
Manchester City v Huddersfield Town
Blackburn Rovers v Cambridge United
Gillingham v Sheffield United
Swansea City v Morecambe
Chelsea v Preston North End
QPR v Bournemouth
Coventry City v Oxford United
Brentford v Wolves
Plymouth Argyle v Sutton United
Maidstone United v Stevenage or Port Vale
Newport County or Barnet v Eastleigh or Reading
Hull City v Birmingham City