The Blues are unhappy at being asked to play two league games in the space of 72 hours after their trip to Goodison Park was rescheduled for television.
The club insist the change, which sees the game put back two days to Thursday April 17, "undermines the sporting integrity of the competition", as it comes three days after they host Wigan.
Chelsea will use the TV money gained from the game to pay for tickets and travel for their supporters.
Chelsea spokesman: "We've continued to make very strong representations for the date of the Everton away game to be changed. This now seems unlikely.
"Under these circumstances, Chelsea believes it would be inappropriate to profit from the television fee for this match as per normal."
Chelsea have been allocated 2,900 seats for the game and will offer refunds to fans who have already bought tickets.
They also plan to pay for train or bus tickets to get supporters to and from the game.