I'm not creating an original theory here. This one has been floating around on the internet for a while now. But it's an interesting concept. Qui-Gon Jinn was the driving force (no pun intended!) behind Anakin's rise to the Jedi Order and, arguably the creation of the greatest Sith Lord the galaxy has ever known, not to mention the downfall of the Republic. Which, if he was a Jedi, would make no sense at all. As a Jedi, his first duty is as a defender of the Republic. But the Sith have no such obligation. On the contrary, they are dedicated to the downfall of the Republic and its ultimate replacement with a new Sith Empire, as there was many centuries before the events of The Phantom Menace. So what if Qui-Gon was a Sith? How would that alter his motives? It certainly would explain some of his actions from the film that otherwise have no logical explanation. Let's look at the facts.
He was trained by Count Dooku (a Sith)
In Attack of the Clones, Dooku comes to an incarcerated Obi-Wan Kenobi and offers him his freedom in exchange for Obi-Wan's promise to join the Dark Side when he is freed. Naturally, Obi-Wan refuses. Dooku states that Qui-Gon always spoke highly of Obi-Wan. Dooku continues that he wishes Qui-Gon were still alive to help him. Obi-Wan argues that Qui-Gon would never join the Dark Side, to which Dooku mysteriously answers "Don't be so sure, my young Jedi." He reminds Obi-Wan that Qui-Gon was once his apprentice. However, if this theory is accurate and Qui-Gon WAS a Sith, this is where the puzzling twist comes in. Dooku says that Qui-Gon would never have supported the corrupt Senate if he had learned "the truth" (that the Senate was being run by Darth Sidious). However, his plea for Obi-Wan to join him in destroying the Sith, while an elaborate ruse, certainly clears up this puzzle. In light of the fact that Sidious, the Sith Lord, was running the Senate, it actually makes sense that Qui-Gon would support him.
Here's that scene if you need a refresher.
See? Makes sense now, right? Dooku's got an elaborate ruse going here, trying to make Obi-Wan believe that he has the Republic's best interests in mind. Which is why he is so quick to use his own apprentice as a bargaining chip. He knows that without bringing in the influence of someone Obi-Wan respects, he will never get Obi-Wan to join the Dark Side. But if Dooku were to portray himself as the savior of the Republic and the Sith (Qui-Gon included) as evil, Obi-Wan would be more apt to join him.
Qui-Gon has a history of defying the will of the Council
Qui-Gon insists that Anakin is the Chosen One and as such, he will train the boy whether the Jedi Council approves or not. Obi-Wan begs him not to, saying, "Don't defy the will of the Council, Master. Not again." Notice those last two words. Not again. This would imply that on at least one occasion, (likely multiple occasions), Qui-Gon has taken this action before. If he is secretly a Sith, his defiance of the Council is much easier to explain. He doesn't answer to them anyway, so what does their opinion matter? Not much, obviously. No Jedi worth his midichlorians would defy the Council on any matter, especially since doing so with enough frequency and vehemence would likely result in expulsion from the Jedi Order. But if Qui-Gon is a Sith, it wouldn't matter if he was cast out of the Order. He'd just run home to his Sith buddies.
He declares Anakin to be the Chosen One
On the surface, this might not seem to be a reason for Qui-Gon to be a Sith, but hear me out. Qui-Gon finds a kid who he clearly recognizes has the potential to be the greatest Sith of all time. He knows that if he brings a random slave child from an Outer Rim dustball to the Jedi Council and asks them to train him, they're not going to go for it unless there is something incredibly special about the kid. So what to do to prevent this and ensure this boy fulfills his Sith destiny? Claim that he is the Chosen One of course! And as a contingency plan, he can just defy the Council's orders and train the kid anyway. Problem solved!
Qui-Gon dies, but makes sure Anakin is trained anyway
Now, at this point, you're probably wondering, "Wait, if Qui-Gon is a Sith, why does Darth Maul kill him?" Never fear, I have an explanation for that, too.
Remember this scene? Yep, that's Darth Maul (a Sith) fighting Qui-Gon Jinn (arguably another Sith). So, if they are on the same side, why are they fighting? Because, at this point, Darth Maul doesn't know that Qui-Gon is a Sith. All he knows is that a guy who looks like a Jedi is attacking him. Qui-Gon has never met Darth Maul before and is unprepared. He manages to climb into the ship and make up a rather lame excuse to satisfy Obi-Wan's curiosity. Meanwhile, Maul travels back to Coruscant, where THIS happens...
At this point, though not shown on screen, Sidious likely informs Maul that Qui-Gon is a Sith and orders him to get rid of Obi-Wan at all costs. Qui-Gon is not informed of Maul's mission and has his own plan to convert Obi-Wan to the Dark Side. Thus, when Maul confronts them on Naboo, Qui-Gon keeps trying to protect Obi-Wan. If you watch the fight scene, you'll notice that with the exception of the fatal blow, every pass that Maul and Qui-Gon make at each other misses completely. Furious that Qui-Gon is interfering with his mission to destroy Obi-Wan, Maul stabs Qui-Gon and attacks Obi-Wan, figuring that Sidious will forgive him in view of the circumstances. However, Maul is brutally murdered and with Qui-Gon's dying breath, he orders Obi-Wan to train Anakin, which Obi-Wan agrees to do. And so Qui-Gon slips off to wherever the Sith go when they die, content that he has fulfilled his mission.