As stated in the previous submission, certain staircases in Final Fantasy push a state on to the stack to keep track of where you have gone. If you go up/down enough, you can overflow the stack. Hitting start to bring up the menu triggers a glitch that jumps into a range of memory that's used when entering the names of your characters. There aren't a lot of staircases that use this but one of them is right where you start, in the castle. For a full explanation see the forum discussion of the previous submission.

There are many ways to beat the game with this glitch. One way is to jump right to the credits by jumping to the memory of the item list. However, it has to be set up a certain way for this and even with underflow glitches it still takes a while (about 20 minutes).
Another interesting but much longer way involves gaining access to the final dungeon with the glitch, and completing it. The stairs glitch can corrupt the thief's level to 103. At that level most normal enemies flee and bosses flee about 2/3 of the time. It takes close to half an hour but that still beats the USA any% TAS by over 20 minutes.
The method used in the previous submission first uses the same level corruption trick. A second glitch causes the next NPC (directly to the left of the stairs) to trigger the final boss fight vs Chaos. The new method used in this submission, found by pirohiko, has a set of names that jump to the end from a different set of instructions, and only requires 32 stair climbs instead of 70. However, you do have to enter the menu before the 32nd stair.
Thanks to pirohiko for finding the route used here. Also, normally, you would need to have your 4th character as a white mage. This time, though, you can keep it at the default, just put the right name.

Samsara: Unfortunately, this run has been bested.

Samsara: Bit late on this, but replacing the file with Spike's conversion/improvement.