They have also made a complaint to the Football Association on the grounds that Bates has broken the governing body's guidelines by referring to Abramovich and his fellow Jewish board member Eugene Tenenbaum and adviser Eugene Shvidler as "a bunch of shysters from Siberia".
The remarks were in connection with Bates' attack on Chelsea's behaviour in their dispute over approaches to three players in Leeds' academy.
They feel his comments about Abramovich were beyond the pale and designed to cause the greatest possible offence.
Chelsea released a statement that read: "Such comments have no place in football, a sport which is rightly committed to fighting racial intolerance and bigotry. Chelsea believes these comments are part of a personal campaign being waged by Mr Bates against our club and his actions cannot be allowed to masquerade erroneously as being in the interests of football as he claims."
Leeds said last night that they were "totally amused" by Chelsea's complaint and dismissed the allegations.