The highest Egg drop without breaking is from 700 Feet

On August 22 1994 David Donoghue threw an egg out of a helicopter onto a golf course in the UK, from a height of 700 feet. Apparently the trick was to get the egg moving forward at the same speed it's falling, then have it land on a grassy slope. Looks like it worked as he now has the record for the longest egg drop without breaking in the world.

Fact Source