I haven't played CE before, so feel free to take my advice with a pinch of salt. That said, I've always thought the best way to play evil is to make a character who truly believes they're doing good - even when in reality they know they aren't. The chaotic part of chaotic evil means they don't approve of the laws of societies and governments, so I'd try and incorporate that too. Here's an example:

A bandit camp's been raiding a nearby village for supplies. Your party is hired to eliminate the menace, and return whatever supplies are present - the village desperately needs them as times are tough and they're running low on food. At the beginning, your character is having doubts in the mission because they're thinking "What good will come even if we remove the threat? The village is doomed anyway - societies always fail."

You fight off the bandit threat, and your character happens to be the one who ends up finding the stolen food. You don't want people in the village to starve, but more than that: you don't want those people to be part of a village at all. So instead of returning the supplies as you promised, you hatch a plan. You dump the contents of the crates and hide the food somehow. When your party arrives, you show them the empty crates and state "the bandits must have eaten it all, or maybe sold it." Why? Well, people wont stay in a place with no food when they're desperate. They'll move on to somewhere else. The village itself will fall, but some of the people will survive.

You return to the village to collect the reward, and spread the word that they'll have to make do with the food they have. Then, you move on with the knowledge that somewhere down the line, the village will be no more. This is a win for your character. You could make the argument that this character is chaotic neutral at this point, but the evidence is this:

Your character has lied, stolen, and likely put innocent people in danger to achieve their goals which (in this case) happen to be overthrowing established governments.

They haven't acted without planning or forethought like many chaotic players are known to do.

Most of all, because your character believes what they are doing is right, they will continue to perform these actions wherever they go. Like many evil people in the real world, they won't be hunted by police or expelled from society. Some people may hold your character in high esteem.

Only you as the player will know the truth: Your character spreads destruction wherever they go, endangering lives for what they believe is right. And that, I feel, would be a feat truly worthy of the name evil.