What is the Golden Chest?

Solution 1:

This chest holds extremely good loot for your level. If you haven't opened the chest yet, wait to open the chest for as long as possible. If you open the chest at max level you'll get great purple or magenta (e-tech) rarity weapons. If you open it too early, you'll have a very good weapon for maybe 5-10 levels, and then it will be useless.

When playing co op with friends new to the game, make sure to warn them of the chest. It's an extremely common problem that people open the chest with no idea that it's special. It does finally have a warning that it will consume your keys when you try and open it now though.

You get the keys by activating your preorder bonus or by entering Shift Codes from GearboxSoftware and Randy Pitchford (President of Gearbox) on Twitter. The promotional ECHOcasts account also posts them less often than the other two. They occasionally tweet Shift Codes which can be entered in game to get keys. They release a couple a week or so. Note that Randy and Gearbox don't post the same shift codes (though the occasionally retweet eachother) so you should follow all 3 accounts if you want all of them. Be quick, shift codes expire either based on time or by how many people redeem them.

Solution 2:

I've opened the golden chest at least a hundred times (hacked key numbers to experiment), and every single item from it has been either purple or e-tech (red-purple).

No legendaries, ever.