All I know for sure is that I read the summary of the story on fanfiction.net, earlier this month, and the summary said something about centuries, and I'm paraphrasing here because I don't remember what it exactly said but here's what it said, "And yes, She." Something like that, also as far as I know it wasn't a Naruto X Kurama fic.
This might be "The Teenage Kyuubi"
And yes, she, the kyuubi is a girl. ... The female kyuubi ... Kyuubi. Now read on. We find the Kaze no torio (I'm using the Kaze no torio for the trio ...
Unfortunately, I've only found this excerpt via cached Google searches. It looks like the author may have taken it down.
Another excerpt from the page, found with a slightly different search:
Wait, maybe this is a trap and they are going to do something awful to ... to write an alternate version of this fanfiction called 'The Creationist', ...
but unfortunately, I haven't found anything that matches that either.
Naruto Genkyouien by Daniel Rush is a likely suspect here. When browsing Naruto fics sorted by Favorites, this one is in the top 100, and its description matches the "Yes, she." point of the question, though it lacks any mention of "centuries".
The nine-tailed demon fox. Its mighty tails can crumble mountains, cause tsunamis, and set things on fire. Lots of fire. It might have been better if she actually were an evil entity bent on destroying the world. Yes, she. AU pseudo-x-over.
Also, Naruto and the Kyuubi do not become romantically entangled over the course of the fic.