Tickets went on general sale on Tuesday, having been on restricted sale last week, and sold out within hours.
Fans had queued outside Glanford Park from as early as 3am to ensure their place at Stamford Bridge next month.
It means hundreds of fans who were ineligible for the early purchase and unable to get to Glanford Park in the early hours of this morning have to miss out.
Unlucky fans have already been on the Iron-Bru.net messageboard calling for the club to review their ticket sales policy for big games - the current system was introduced after the fiasco of the FA Cup game against Leeds two years ago.
The only remaining tickets are for a hospitality package costing £150 per person, anyone wishing to order a place should contact commercial manager Michelle Harness on 01724 747678.