The Blues beat Manchester United 1-0 at Wembley in May thanks to an Eden Hazard penalty, in what proved to be Antonio Conte's last game as head coach.
Championship Forest were 4-2 winners over Arsenal in the third round last season and Unai Emery's men could have a venture into the unknown if Solihull Moors of the National League can overcome League One Blackpool in a second-round replay.
City's neighbours United are also at home to Championship strugglers in the form of Reading.
Tottenham, still seeking their first trophy under Mauricio Pochettino, face a trip to Merseyside against either Southport of the National League North or League Two Tranmere Rovers.
Ties will take place between January 4-7.
FA Cup third round – draw in fullBolton Wanderers v Walsall or Sunderland
Millwall v Hull City
Gillingham v Cardiff City
Brentford v Oxford United
Sheffield Wednesday v Luton Town
Manchester United v Reading
Everton v Lincoln City
Tranmere Rovers or Southport v Tottenham
Preston North End v Doncaster Rovers
Newcastle United v Blackburn Rovers
Chelsea v Nottingham Forest
Crystal Palace v Grimsby Town
Derby County v Southampton
Accrington Stanley v Ipswich Town
Bristol City v Huddersfield Town
Wrexham or Newport County v Leicester City
Fulham v Oldham Athletic
Shrewsbury Town v Stoke City
Solihull Moors or Blackpool v Arsenal
Manchester City v Rotherham United
Bournemouth v Brighton and Hove Albion
West Ham v Birmingham City
Woking v Watford
Burnley v Barnsley
QPR v Leeds United
Sheffield United v Barnet
Norwich City v Portsmouth
Guiseley or Fleetwood v AFC Wimbledon
West Brom v Wigan Athletic
Middlesbrough v Peterborough United or Bradford City
Wolves v Liverpool
Aston Villa v Swansea City