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Anakin is the chosen one, even though he turns to the dark side. Why?

First of all, the prophecy states that the chosen one will bring balance to the force. Balance is different than all light or all dark.

When Anakin killed the Jedi and executed Order 66, the light side of the force succumbed to the dark side. He then and fulfilled half of the prophecy. Some say that Luke proves this wrong. Actually, Luke never technically became a Jedi Knight. He had the skill, but not the rank, so he didn't count.

When Anakin became a sith, he was in charge of the armies and officers. He let them destroy the what was left of the light side until the good in Anakin was the only true "light side" that remained.

When Anakin defeated Darth Sidious (or the Emperor, your choice), he was the only "dark side" remaining. Both sides of the force died with him. Without anyone to command them, the rest of the Empire fell apart. At that point, the force was equal. He destroyed the Sith and the Jedi, bringing the force to balance. This makes him the chosen one.

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In addition to this, the force-wielders on Mortis proved that Anakin was the Chosen One. He was able to tame both the Son and the Daughter, a talent entrusted to the Father. The Father held a test to prove Anakin was the Chosen One, and Anakin passed.

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Also on the planet Mortis, Anakin was in some way responsible for the death of all three force-wielders. By doing this, he brought the force to balance.