The lucky egg is an item that can be held by wild chansey. If equipped, you get +50% experience gained from battles. There is a 1 in 20 chance that a wild chansey has this item. Chansey itself has a 4% chance to show up in the safari zone, 5% if you use the repel trick.

I have captured 70 chanseys in the safari zone so far (having encountered 377 chanseys in the process, 80% run away). Where the FUCK is my lucky egg