What is the chronological order of the storyline in the Five Nights at Freddy's series?

Game 2 -> Game 1 -> Game 3

Backstory

Before any game

The first restaurant closed after a child was murdered on the front steps, who then possessed the Marionette. (see the cake death game)

Game 2

The animatronics were bought, and a new restaurant opened. The old animatronics were taken apart for parts for the new animatronics. The new ones had facial recognition, and were tied into a criminal database.

• The 'purple man' killed 4 children in between nights 2 and 4. They possessed the old animatronics.
• The purple man also reprogrammed the new animatronics.
• They were suspicious of him, and he made them not attack him.

This restaurant went out of business because of strange behavior from the new animatronics. The new animatronics were scrapped (because of the tampering) , but the old were kept around for the possibility of a new restaurant.

Game 1

The 3rd restaurant is opened, and no mask was provided for the guard, because the purple man used Golden Freddy to lure kids in to kill them.

Phone guy dies night 4.

Game 3

This game is set ~30 years later. Somebody makes a haunted house around the Freddy Fazbear franchise. .

This game, through the minigames between nights, allows you to figure out the rest of the plot, but is not itself much of the plot.

I think its 2, 1, 3.

Phone Guy Dies in 1, but is there in 2. And 3 states its 30 years later.

The game theorists did a video explaining if FNAF 2 is a prequel or a sequel; the result they get is prequel.

Both videos are really interesting. I highly recommend watching them. (and the second seems to still works with the story of FNAF 3)

It could also be 1, 2 then 3.

The second game appears to occur after the first game.

From Steam's main page on the second game (http://store.steampowered.com/app/332800/):

About This Game

Welcome back to the new and improved Freddy Fazbear's Pizza!

In Five Nights at Freddy's 2, the old and aging animatronics are joined by a new cast of characters. They are kid-friendly, updated with the latest in facial recognition technology, tied into local criminal databases, and promise to put on a safe and entertaining show for kids and grown-ups alike!

What could go wrong?

As the new security guard working nights, your job is to monitor cameras and make sure nothing goes wrong after-hours. The previous guard has complained about the characters trying to get into the office (he has since been moved to day-shift). So to make your job easier, you've been provided with your very own empty Freddy Fazbear head, which should fool the animatronic characters into leaving you alone if they should accidentally enter your office.

As always, Fazbear Entertainment is not responsible for death or dismemberment.

The third game appears to be the latest in the series.

From Steam's main page on the third game (http://store.steampowered.com/app/354140/):

About This Game

Thirty years after Freddy Fazbear's Pizza closed it's doors, the events that took place there have become nothing more than a rumor and a childhood memory, but the owners of "Fazbear's Fright: The Horror Attraction" are determined to revive the legend and make the experience as authentic as possible for patrons, going to great lengths to find anything that might have survived decades of neglect and ruin.

At first there were only empty shells, a hand, a hook, an old paper-plate doll, but then a remarkable discovery was made...

The attraction now has one animatronic.