Back in the early 1990s, Chris Houlihan was a reader of "Nintendo Power" (the official Nintendo magazine). Before the release of Zelda: A Link To The Past a.k.a. Zelda 3, Nintendo Power held a contest, where the winner would have his name in a secret room inside the game... and the room would be so well hidden that it would be nearly impossible to find. And indeed, it nearly is, unless you know where it's at. In fact, it seems we had to wait for the internet / Snes emulators era for the room to be found by anyone at all.
Here's what you have to do, there are different methods to enter the room:
FIRST (EASIEST) METHOD:
1. First of all, you need the Pegasus Boots! If you don't have them, go get them and come back here.
2. Start a saved game and start at the Sanctuary.
3. Now, you're going to have to go to the secret entrance to the Hyrule castle (the one behind the bush you go to at the very beginning of the game) AS FAST AS POSSIBLE. The trick will only work if you're fast, which is why you need the Pegasus Boots. Try to storm your way through the screens.
4. Here is the exact path [note that any path is theorically good as long as you reach your goal quickly enough, but this one works fine for me]: go down to leave the Sanctuary, down past the cemetary, then left. In the new screen, go down as soon as possible, and you will enter a difficult area with big trees, rocks, bushes, and enemies. Proceed with caution here, as it's easy to waste time if you're not careful enough. Go right of that screen. You are now at the Hyrule castle. Go down, then right, and go past the main entrance without entering. Keep going right until you're at the eastern side of the castle, then go up. You will find the bush leading to the secret entrance. Get rid of it and drop down the hole, and IF you were fast enough, you will enter the Chris Houlihan room.
It's a room filled with blue rupees and a plaque saying : "My name is Chris Houlihan. This is my top secret room. Keep it between us, OK?"
If you enter the normal underground castle passage, it means you were too slow.
SECOND METHOD:
It's the same principle, but instead of starting from a saved game at the Sanctuary, from anywhere in the game just go to the Kakariko village, taking as long as you wish. There, you have to place yourself at the top of the dirt path leading to the fortune teller screen. The race against the clock starts now: run up to the fortune teller screen and go to the secret passage behind the bush just as in the first method (go right and then it's all the same directions), always running as fast as possible. This method is more difficult for me than the first one as it requires you to be even faster, but I have tried both and they *both* work.
OTHER METHODS:
Other methods have been referenced on the net, and I won't reference them all here as they haven't all been verified and the methods mentioned above work fine. It seems you can also access the room by falling into a certain spot at the Pyramid in the Dark World (but the people who have done this don't know how to do it again), or by using a bomb to push you down a secret passage in the cemetary. Some also say the "time attack" methods won't work if you get hit by an enemy on the way. This might be true, but I wouldn't know because I usually started from scratch after getting hit, since it makes you lose precious time either way. There is a rumour the egg only appears when the game somehow malfunctions (instead of giving you an error message, it warps you to the Chris Houlihan room), which could explain why the ways to enter the room are so strange and different.
The "do it twice in a row without taking the rupees and next time you will get a chest with 500 rupees" thing, referred to in the comments for this egg, hasn't worked for me (I've done it but the room was identical) so until we see screenshots I'll assume it's a hoax.
jut gemacht 
