TL;DR: it's the Creator.
Word of God
On 11 July 2010, Brandon Sanderson said he knows the answer:
STEFAN: So we know in The Eye of the World, there was somebody who talked in capital letters like how the Dark One did. Obviously you can't tell us who it was, but will we know by the end of A Memory of Light?
BRANDON SANDERSON: I know what that was about. Will it be in the next book? Er...RAFO. Sorry.
STEFAN: Will we know by the end of the series though?
BRANDON SANDERSON: I really can't say yes or no. This is one of the things Harriet has asked me to be very quiet about.
On 12 January 2011, he made a direct statement that he's not going to tell us (i.e. presumably RAFO):
BRANDON SANDERSON: No, I'm not going to tell you what the VOICE at the end of The Eye of the World was. Lots of people like to ask, though.
And then on 8 February 2013 we have a solid "don't know":
Brandon [...] said that many people think the voice in all caps in The Eye of the World is the Creator, which might indicate the Creator was, but stated it really wasn't known even in-world.
And on 13 February 2013, we get some actual information:
QUESTION: So, at the end of The Eye of the World, the all caps voice? Will we ever find out who it was, or what they were looking for?
BRANDON SANDERSON: The all caps voice at the end of Eye of the World makes an appearance in A Memory of Light.
So all you have to do is find an all-caps voice speaking in aMoL!
And here we have it:
IT IS TIME. LET THE TASK BE UNDERTAKEN.
The voice spoke with the inevitability of an earthquake, the words vibrating through him. More than sound in the air, far more, the words spoke as if from one soul to another. Moiraine gasped, eyes opening wide.
Rand was not surprised. He had heard this voice once before, and he realized that he had been expecting it. Hoping for it, at least.
“Thank you,” Rand whispered, then stepped forward into the Dark One’s realm, leaving footprints of blood behind.
Rand "had heard this voice once before" - this, together with Sanderson's quote from 13 February 2013, makes clear that this is the same Voice.
The last thing Rand says before this voice arrives in tEotW is "The Light blind you, Ba'alzamon! This has to end!" This gives us a clue as to what the "it" in "IT IS NOT HERE" refers to: the Light. The Voice is saying the Light cannot reach to the place where Rand now is.
The two main theories for the identity of this Voice are the Creator and the Dark One. But "I WILL TAKE NO PART" definitely doesn't sound like the Dark One. The whole business is about him trying to take part, to break free of his prison and touch the world once more. He wants to take part to the maximum extent he can, whereas this voice is unwilling to take part directly.
What about "ONLY THE CHOSEN ONE CAN DO WHAT MUST BE DONE, IF HE WILL"? Well, the "chosen one" is obviously Rand. The prophecied Last Battle is meant to be between the Dragon Reborn and the Dark One. The Dark One doesn't "choose" anybody to fight his fight for him, but the Creator does.
So I think it was the Creator.
A quote that may or may not support this:
The Creator is completely removed from the world; aside from...creating...the Pattern, he does nothing else whatsoever to influence anything.
This fits perfectly with "I WILL TAKE NO PART", although admittedly it doesn't mesh too well with the fact that this Voice is talking to Rand at all.
And finally, the quote from aMoL makes this pretty clear: Rand was "hoping" for the voice, and whispers "Thank you" to it. That's not the Dark One. That's the Creator, giving his blessing to his champion just before the Last Battle.