Cape Town - The FA Cup sixth round draw was made at Stamford Bridge on Sunday evening, with the competition heading into its quarter-final stage.
The draw sees Crystal Palace away to second-tier Reading, a club once managed by Eagles boss Alan Pardew.
Chelsea, who beat an under-strength Manchester City 5-1 at Stamford Bridge, are away to Everton in a repeat of the 2009 FA Cup final which the Blues won during current caretaker boss Guus Hiddink's first spell as interim manager.
West Ham, who in Sunday's opening fifth round tie saw off Championship Blackburn Rovers 5-1, will travel to the winners of Monday's tie between third-tier Shrewsbury Town and struggling Manchester United.
Meanwhile holders Arsenal, bidding to become the first club to win the FA Cup three years in a row since the 19th Century, must see off Hull in a replay following Saturday's goalless draw at the Emirates if they are to face Watford in next month's quarterfinals.
FA Cup quarter-final draw (Premier League unless stated):
Reading (II) v Crystal Palace
Everton v Chelsea
Arsenal or Hull City (II) v Watford
Shrewsbury Town (III) or Manchester Utd v West Ham United
Ties will be played 11-14 March.