According to the SRD:
"Evil" implies hurting, oppressing, and killing others. Some evil creatures simply have no compassion for others and kill without qualms if doing so is convenient. Others actively pursue evil, killing for sport or out of duty to some evil deity or master.
As you can see, an evil character need not actively pursue the "cause" of evil. He may simply have no compassion, and act purely out of his own interests and goals. Selfishness can be extremely evil when expressed in this manner. If murdering thousands of innocent people to achieve his goals will result in a quicker or more effecient way of achieving an evil characters goals and/or plans, he will do so without any hesitation or remorse.
After all, what are they to him? Evil people generally view people not personally connected to them as pawns for their plans or pleasure, or nuisances and inconviences to be disposed of. Chaotic characters are very independent, so a CE character can be very difficult to play in a party of adventurers seeking to do good in the world. The only reason a CE character would do so is if he saw a great deal of profit or power to be gained from such. Try and work that into your characters motivations for staying with the party.
A CE character would likely refuse to acknowledge the authority of any of the other party members, and indeed, of the party itself. The only reason he would ever acquesiece to the rest of the parties desires is if he felt not doing so would result in a loss of power/profit, or endanger his own life. You should try and find a way to do this that will not result in you getting killed/kicked out of the party, but it may be hard, depending on the makeup of the rest of your party.
Just remember, even CE people can have friends, but it's likely they would dispose of those friends in a heartbeat if it gained them a greater degree of power, profit, or furthered their goals. It would be difficult to play such a character, as I said earlier, but it can be done.