Just get a shoe box, and fill it with cotton balls and packing peanuts. Project, finished.

I did this in 7th grade biology.

Make something that very carefully cushions the egg on all sides. Has a large flat light-weight bottom that will dramatically decrease its rate of descent.

Keep to these two principles and you will win.

...or...

You know those toy army men with parachutes....

Take one of those and just tie the string around the egg. Maybe wrap the egg in a few layers of light weight cushion.

I have done something like this, an egg was dropped from the balcony, and we had to make something that would catch it. However, the guy dropping our egg missed, so we never got to test it out....

Basically, you want something that will make the deceleration less sudden, so increase the distance it travels when it is slowing down, decreasing the force on the egg. I'm not sure how this could be acheived, but you want something along the line of a crumple zone (or something that would acheive the same effect)

Styrofoam? I dunno I just like that word....styrofoam....yeahhh.

We put eggs inside nose cones for rockets that went ~500-1000 feet. One cone broke off and smashed into the ground so hard the 9V battery for the altimeter crushed. All they packed it in was Styrofoam and it survived. It really isn't a hard project. do it youself

C'mon Soriku, you're in the smart class. You should be able to get based on my very good hints.

I got an A, btw.

Water container???

The base should be large, flat, light weight, and be able to bend or curve from the air resistance as it falls. This helps it not to turn sideways and fall faster, thus breaking egg.

The container holding the egg should be securely fastened to the egg and center of base. There should be soft cushion between the egg and the container to reduce the jolt from landing.

Also, if possible give it a spin when you drop it so it kinda works like a frisbee. :)

That is as far as I am going to tell you. The rest is part of your learning curve.

Hint: Use swimming arm bands and put the egg inside. That should allow you to drop it from a high balcony and not break it.

Edit: Pic insert.