How do I obtain more Golden Keys for Golden Chest(s)?

To get another Golden Key you can register at http://shift.gearboxsoftware.com and create a new character. Then select your old character and enter the shift code you were emailed from linking your email and Steam account to SHiFT.

Also, be sure to follow Gearbox Software on Facebook and Twitter. According to Randy Pitchford, President of Gearbox, they plan on doing code SHiFT code giveaways to add more Golden Keys via these official sources in the future. (source) They have several keys a week so far, usually a couple each day on Saturday/Sunday. They're still testing the concept according to Pitchford, so they may change how they do things.

As of October 2nd, 2012, Duval is still sending out SHiFT codes on his Twitter in an effort to test out the software that will eventually be used for the giveaways. Since he is just testing the software, this could stop at anytime though.

UPDATE: The developer has patched this so that this Golden Key hack does not work on the PC anymore. The console hack does still... so far.

If you're on the PC you can go to directory of the game then go to DLC, then premium club, then open the WillowDLC.ini with Notepad and edit it to:

[GoldenKeys]
+SourceId=254
+NumKeys=300

[PromotionalUnlocks]
+UnlockId=2

this will give you around 260 keys to use at your will

For Xbox 360 and PS3 watch this video for unlimited keys

On the PC version of Borderlands 2 your save data is broken into two parts: profile and character save. The profile contains shared information between your characters such as bad-ass achievements, skin unlocks, and the golden keys.

Your character save contains weapon load-outs, current location, and class tree info. Try deleting your profile and starting a new game with a new character. This should give you a new key. Then import your old character save into the new profile to access the key. Note: You will lose all information attached to your current profile if you delete it so back it up first.

This work around can also be used to unlock the chest as many times as you like. Also, your save data should be located in: documents/mygames/borderlands2/willowgame/savedata for those who don't know.

Here's a fix for those who didn't get emailed a shift code; go to shift.gearboxsoftware.com and unlink your Steam account. Then go into Borderlands' main menu, then Extra, then Shift. Sign in here and you should get your golden key without the passcode they don't seem to actually send out.