Chaos Terminators are the MORE EVIL AND SPIKIER counterparts of the trusty Terminators of the Imperium of Man. They're sometimes known as Tuskies or Elephants, due to their odd but pretty cool placement of tusks on their helmets; whether they got them from hunting down space elephants or grew them naturally from the Warp is unknown. They are grizzled veterans who fight wearing the widespread Tactical Dreadnought Armour of the Chaos Space Marines.
Due to either expenses, lack of salvageable tech, or just doctrinal preference, Chaos Terminators surprisingly wield standard power weapons far more often than Power Fists and Chain Fists, which are THE standard weapon of Loyalist Terminators. In addition, due to corrosive effects of the warp, choleric temperament of their machine spirits, and bastardization with other suits for repairs, Chaos Terminator Armor is incredibly rugged and individualistic; a disturbed reflection of the engineered killer who dons it. The Armor also overwhelmingly dates back to the Horus Heresy, since producing new suits is stupidly expensive and time-consuming given the Logistic nightmare that is the Eye of Terror. Even then, the new suits are often worse than their old beat up suits, as many of their more complex components cannot be replicated anymore. Additionally while they have betrayed the Imperium the adepts of the Dark Mechanicus are still tech-priests at heart, and would rather fend off an Imperial Guard regiment with a rusty servo arm, than part with anything more complicated than a boltgun. Hence even if the fallen techpriests managed to restore a Terminator armor to functioning condition, trying to bargain it off them without the backing of a major Chaos figure is a challenge in itself.
While not the swiftest of troops as they are motherfucking Terminators, they can (Like their loyalist counterparts] use a Land Raider to travel across the battlefield to positions which their weaponry will make the best impact. Otherwise they can teleport through the use of arcane technology or sorcerous powers. They often wait for the perfect moment to strike, poised to eliminate the target when at his most vulnerable.
They are also among the most favored servants of the Chaos gods. This is mainly due to how Chaos Terminator armor obtained: it is very, very unlikely a Chaos champion will simply be granted Terminator armor, even if they have millennia of experience and victories under their belt. The only real way to get a suit is to kill another Terminator, either a veteran of the old war who's worn it since the Great Crusade (and thus is very proficient in its use), a loyalist Terminator (who would be one of the elites of the chapter), or another chaos champion who managed to swipe and wear it (who has fought life and limb to pry it off someone else and keep it that way for centuries). In either case, any would-be champion able to best the former wearer in combat, drag their corpse into the warp, and somehow stave off the dozen OTHER aspiring champions who would want the armor is a proficient warrior of few equal.
Hence, Chaos Terminators enjoy a fair bit of power amongst their warband, many of them have the honor of being in their Chaos Lords' personal retinue and act as their enforcers. A lot of the rank-and-file tend to hate them, as termies tend to abuse their position, but many also see them as goals to strive for, as the wearer of the armor most likely started out as another no-name Chaos marine just like them: there's nothing stopping anyone from becoming a Chaos Terminator themselves, apart from skill, aspiration, and more luck than most people are granted with in a lifetime in the grim darkness of the far future.
The standard Chaos Terminator armament is a Combi-Bolter and a Chainaxe which can be upgraded to either a Power Axe, Power Maul, Power Sword or more rarely, a Power Fist or Chainfist. In addition, Terminators may also take a Reaper Autocannon or Heavy Flamer in place of their Combi-Bolter. The Combi-Bolter itself can be configured to function as either a Combi-Meltagun, Combi-Plasma Gun or Combi-Flamer.
They can also be equipped with a pair of Lightning Claws for close combat.
Two general facts about Chaos Terminators: they have always been there since the beginning and they have also always been the premier elites (or equivalent) choice for the Chaos Space Marines. Of note, they are tough, they pack a lot of dakka and they hit hard in close combat. What has always set them apart from their loyalist counterparts is the weaponry loadout and availability with a little help from the dark gods, even back in the Rogue Trader days. There are no assault terminator variants so chaos termies are known for mixing up CC weapon and shooting weapon loadouts, their preferred ranged weapons being the combi-bolter, other combi-weapons and either a heavy flamer or the well-known reaper-autocannon for special weapons. They're also known for being cheaper than loyalist termies as they pack power weapons default instead of power fists. Second Edition termies were basically the same, sporting higher weapon skills, attacks, wounds and their namesake terminator armour, which back in the day was 3+ on 2d6 back then (no invulnerable). With some deity goodies, they were the go-to support choice albeit on the expensive side and even more so if riding in a Land Raider, their other preferred transport option next to Teleport Attack (aka Deep Striking).
Third Edition Roller-Coaster
Terminators in general took a battering in third edition, especially for chaos. Reason being, deep-striking units could only fire assault weapons when deep-striking (initially, but this was changed later), meaning combi-bolters were unusable for striking termies. Also was the introduction of the 5++ and the reduction of termie statlines down to PAMs with another attack, a better save, deep-striking, the total loss of grenades, no pistols and the ability to move and shoot heavy weapons (unless deep-striking). Termies had to compete hard against Veterans, Berserkers, Thousand Sons, Plague Marines and chaos dreadnoughts in the elites slot, though the first four of these could be shuffled to troops with a choice of HQ. There are also options for cult terminators which were fleshed out more fully in a FAQ, but they pail in comparison to 3.5. Speaking of, that book merged Chosen and Terminators together with terminators being an upgrade to chosen. There's a lot to say about how awesome and skubtastic this was, but suffice to say that these were some of the earliest roots of what will eventually become Death Guard and Thousand Sons special terminators (and hopefully more to follow). It was also in 3.5 that rules for deep-striking were amended to allow them to shoot any of their weapons - basically, if you can normally move and shoot, you can deep-strike and shoot. Unfortunately, Terminators had to compete with the original, uniquely chaos TEQ in 3.5 - the Obliterators, which GW thought would be great to move into the Elites slot this time around. FWIW, oblits were just flat out better terminators in 3.5 if they could be afforded, though most armies could only take one squad of oblits.
The Age of Termicide: Fourth through Seventh Editions
Basically, 4th edition either nerfed everything in the elites slot for CSM or they were moved out into other slots, leaving them largely as the only viable elites option. This state of affairs persisted for 3 (possibly 4) editions, but 8th is somewhat special. Weirdly enough, termies didn't change at all (aside from being split off from Chosen, who were arguably the only other serviceable elites choice for CSM) - everything else around them did! Along with the nerfing of CSM units, the rules changed granting termies the ability to shoot their weapons, without penalty, after deep-striking. Which was great - you loaded up your boys with guns, plopped them down (with ease with icons guiding deep strikes) and blast what needs blasting! Combi-plasma was also introduced as a weapon option for termies increasing the punch for a turn of shooting against the Space Marine Meta. Or you could take Combi-meltas if there's a tank that needs opening or Combi-flamers, but they would need 6th-edition and overwatch to truly make them useful (ACTUALLY, deepstrike a terminator unit with 5 template weapon was devastating even before 6th BUT it was tricky getting into place and very situational).
Eighth Edition: Enhanced Termicide
Termies just got buffed - 2 wounds per model, combi bolters are rapid fire 2, other combi weapons are no longer one shot and both profiles can be fired simultaneously. Oh, and they can charge after deep-striking (tricky needing to make 9" on 2d6, but still). Truly, everything got a buff in this edition eventually, but termies are still better than most other choices due to their versatility. They don't really need any stratagems to make them playable and their pretty scary when they are used on them; they don't require synergy with the rest of the army but can synergize rather well with them, especially with Termie Lords or Sorcerers.