With Great Difficulty, But....
But: That Article Is Extreme
Unfortunately for my pithy header, the "but" clause has to come first. I (and evidently many others) take exception with Easydamus' description of chaotic evil. It's not wrong, per se-- the mindset it describes does qualify as chaotic evil, but it's an extreme and cartoonish example of it that just will not work as part of a D&D group, because it's a murderous snotball of hate and violence.
Since you've tagged this with 1e and 2e D&D, it's worth going back and looking at what those systems have to say. I'll content myself with 1e, since I don't have access to a 2e DMG. It's also worth pointing out that in these systems, although it's often unspoken, alignment operates at three only hazily defined levels.
It operates at a cosmic level, with all of the outer planes conforming to it-- this is where we get pure chaotic-neutral monsters of weirdness like Slaad, inflexible lawful-good angels, rigid hierarchical lawful evil devils who won't/can't break a contract, etc. This isn't what we're talking about here, but that article could almost be describing the mentality of a chaotic-evil demon or demon cultist rather than a real person who is a functioning member of society.
It operates at a societal/social level, concerning itself with the amount of a law necessary to have a functioning society in some given environment, and the necessary protections one person (or group) has against others before things fall apart or bloodbaths start happening. This is kinda what we're talking about, as the PC interacts with the micro-society of his or her adventuring companions, or the larger society in which they are embedded.
It operates at a personal/psychological level, concerning the way the character's mind works, what he or she wants, and what they're willing to do to get it. This is exactly what we're talking about.
That said! The 1e DMG describes both the law-chaos and good-evil dichotomy as (in my opinion) different takes on the others-self dichotomy. Good and evil is about the use of power; power (almost definitionally) accumulates in the hands of the powerful. Good uses that power to safegaurd the weak; evil does not care and by direct implication focuses on self-gratification or perhaps the gratification of a master they are not strong enough to overthrow. This is not my personal take on good and evil, but what I believe is a direct but useful paraphrase of the DMG itself:
Basically stated, the tenets of good are... creature rights. Each
creature is entitled to life, relative freedom, and the prospect of
happiness. Cruelty and suffering are undesireable. Evil... does not
concern itself with rights or happiness; purpose is the determinant.
Law and chaos is about social (for the the purposes of this discussion) cohesion-- law wants more of it, chaos wants less of it. Lawful good and evil may want to leverage the power of a society to more effectively safeguard the vulnerable, or to extract personal utility from them, respectively; chaotic good and evil will lean the other way and believe that individuality and going it alone (or going rogue) will better achieve their moral desires.
Finally, another direct quote from the 1e DMG on chaotic-evil:
The chaotic evil creature holds that individual freedom and choice is
important, and that other individuals and their freedoms are
unimportant if they cannot be held by the individuals through their
own strength and merit. Thus law and order tends to promote not
individuals but groups, and groups suppress individual volition and
success.
That's a bit philosophical for my taste, but the core of chaotic-evil is there: CE doesn't care about the rights, thoughts, or feelings of other individuals unless they are strong enough to make the CE individual care; and groups and societies are always making up and trying to enforce stupid rules, so why bother? If they lead groups, those groups won't tend to be real, functioning societies, but direct extensions of the strong leader's will-- cults of (evil) personality, brigand bands where everyone is afraid to step out of line, etc.
But what is strikingly absent in that description is a lot of the stuff that Easydamus talks about-- they're not required to go forth and kill, or steal everything that isn't nailed down, or corrupt the innocent, or kidnap all the farmers' daughters, or lie pathologically, or punch ever city watch member in the face. None of that psychopathy is even mentioned.
And even the Easydamus article admits this. If you take one thing away from it, take this:
A chaotic evil being is not expected to go about insanely slaughtering and torturing everyone he meets, for he isn't usually stupid. He will realize the consequences of such activities....
and ignore even the end of that sentence:
...and will participate in such pleasurable distractions only when safe from discovery.
Because even that isn't true.
With Great Difficulty
So with all that in mind, playing a chaotic evil character in a group is still hard, and I'll generally disallow it in anything resembling a conventional D&D game. Because let's face it: The 1e chaotic evil PC is not necessarily a snarling, barely-leashed murderbot just waiting for the party to turn their backs before dropping another mutilated body at the village they're leaving.... but they are probably Class One Thousand Jerkwads. Argumentative, always looking for maximum personal advantage at minimal personal risk, never inclined to take one for the team, definite tendency to be obnoxious to important NPCs as well as PCs.
And God help the party if the chaotic-evil guy is the rogue or a spellcaster, because the opportunities for petty crime, and therefore getting caught, will be endless.
What the player has to do, really, is successfully walk a very very fine line where the character is a jerk, without being so much of a jerk that the player becomes a jerk because the character is ruining everyone else's fun. Implicit in that statement is that the player of the chaotic-evil character has to care about the other players having fun. In my experience, I rarely see the players of chaotic-evil characters bring that to the table.
Goals and Consequences and Arcs
After all that, some concrete advice for how to make this work. But I'll be up front and blunt about this: While this is the best advice I have after decades of gaming, I don't think it's very effective advice. I just don't think chaotic-evil PCs work very well-- I won't allow them in my games without a very good reason, and as a player I'll probably walk if I know someone insists on being chaotic-evil. Life is too short.
Goals: Even chaotic evil characters have goals, and hopefully it's not "Build a pyramid of human, elven, and dwarven skulls." If the chaotic-evil character has a goal (revenge against the bigger badder evil is evergreen, here) and realizes that being in this party is the best way to achieve it, that can sometimes provide enough cohesion to keep things together. But it usually has to be a goal that isn't objectively evil, and it can constrain the way you put the game together. (I.e., if your group starts out as, for some reason, the chosen group to go deal with the Big Bad that needs revenging, fine. But if your characters randomly meet in a bar, that probably won't work. It's a spectrum.)
Consequences: Sort of the opposite. Sometimes it can work if there are consequences to not being a Team Player-- staving off the destruction of the world, preventing the demon apocalypse. Sometimes it's as simple as the presence of someone stronger threatening to knock the character's head off if they don't keep in line. It's very awkward if that person is a member of the group, but maybe the chaotic-evil character's boss gave them a job, and by God they're going to do it.
Arcs: This is a weasel way out of it, but maybe the character is interested in playing a redemption or an awakening arc, where they start out chaotic evil and then (relatively early in the game) something happens that shocks their conscience into change, with much of the rest of the game (for that character) being about that. I've seen this happen with lesser versions-- chaotic- or lawful-neutral to good, and I'm actually trying to pull it off right now. But especially in a full evil transition, it's something the GM would probably have to be in on, and it might need to be something the players are aware of so they don't just say, "This is distasteful-- I'm out."
