Acids, such as vinegar, react and dissolve calcium carbonate, which is found in eggshells, to produce carbon dioxide gas and dissolved salt; a protein membrane around the egg remains, creating a springy feel. TV crafter Jim "Figgy" Noonan shares his educational how-to.
Source: The Martha Stewart Show, January 2012
For added experimentation: Pour off the used vinegar, wash the container, and refill with fresh vinegar. Add the “rubber eggs” to the fresh vinegar and set aside. After about a week’s time, remove the egg from the vinegar and note how the size of the egg has changed.
Tip: This experiment can also be done with chicken bones. Follow the instructions as above, leaving the bones in the vinegar for 1 to 2 weeks. The calcium carbonate in the bones dissolves, leaving behind mostly collagen and other connective tissue that is flexible and rubbery.
Raw chicken eggs
Place raw chicken eggs in desired container.
Fill container with vinegar until eggs are completely submerged.
Set container aside for 12 to 15 hours. During this time, the acetic acid in the vinegar will react with and dissolve the calcium carbonate in the shell of the egg, releasing bubbles of carbon dioxide. There will also be a bit of muck on the surface of the vinegar. Only the inner membrane of the egg will be left behind.
Once the shell of the egg is completely dissolved, carefully remove the egg from the vinegar. Note how the egg has changed and how it feels in your hand.