Is there a chapter of Chaos marines that have fallen completely to the Black Rage and are still active?

Question

Looking for a Chaos marine chapter that has descended from the Blood Angels and has completely fallen to the Black Rage, and are still active in some way.

Maybe used as shock troops by anther chapter?

Does such a chapter exist?

Answer 1

Blood Drinkers comes close, although they haven't fallen to Chaos (yet):

The truth behind the Blood Drinkers is far more insidious however. By M37 the Blood Drinkers were a dying chapter, brothers succumbed to the Black Rage as soon as they were fully initiated.

However the truth behind the Rite was that Holos was visited not by an angel but by a Daemon, heavily implied to be Kairos Fateweaver, who made a deal with the battle-brother. In exchange for the blood drinking Rite that would save thousands of brothers from the Death Company, Kairos would gain the ability to change the visions of a select few Death Company marines from the normal visions of Sanguinius' death to those of Holos and the daemon itself. As of M39 eighteen brothers had witnessed it, and Kairos has spoken through the memories to each battle-brother, tempting them with the power of Chaos. If one even so much as thinks of accepting Kairos's offer the entire Chapter will be damned and fall to Chaos. Thus far all have refused Kairos, but the Daemon cares not as only a single "Yes" is necessary for the Blood Drinkers to be damned forever. Only the Reclusiarchs know the truth behind the Rite, though it is unknown if they wish the Chapter to fall.

So, there is a chapter at risk of falling to Chaos with a nigh 100% of the Space Marines that fall to the Black Rage when they are fully initiated. Only the rite keeps them from that and it takes only one battle brother to be tempted for the entire chapter to fall to chaos.

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To the extend of my knowledge, there is no Blood Angels successor chapter that has fallen to chaos as an entirety. Only the Knights of Blood and Flesh Tearers are (AFAIK) not considered as regular Chapters but as Renegade Chapters:

Renegade Space Marines are Space Marines who have turned their back on the Imperium but have yet to fall to the taint of Chaos, differentiating them from Chaos Space Marines.

From the Lexicanum article on Renegade Space Marines

The Flesh Tearers themselves are probably closest to what you seek:

They suffer from a mutation in their gene-seed, making them far more prone to suffer the Black Rage than other chapters with Blood Angels gene-seed. If no cure is found the chapter is likely to be extinct within the next two millennia.

From the Lexicanum article on the Flesh Tearers

Even if there were an entire chapter of Space Marines that has succumed to the Black Rage, it would probably not be very useful to CSM as they can't be led into a specific direction and the toll to capture them for the next deployment would probably the above the gain from such a chapter (emphasis by me):

Rather than face a slow, insane death, Blood Angels will form those who have newly succumbed to the Black Rage into a special unit known as the Death Company. They paint their armour black, daubed with red crosses, signifying the wounds of Sanguinius, and are usually led by the few Chapter officers, notably Death Company Chaplains, who are able to communicate orders to these lost warriors.

From the Lexicanum article on the Black Rage