In a large bowl, mix together the 4 large eggs, minus 1 egg white. (4 egg yolks + 3 egg whites). Beat well with a fork and add a teaspoon of olive oil and salt and pepper to taste. Set aside.

In a frying pan, add 1 teaspoon of olive oil and heat the oil over low heat. Add the fresh crab meat and stir, breaking up the crab into small pieces. Keep sautéing until the moisture is gone and add salt and pepper to taste.

Spread the crab meat even across the pan and pour the beaten eggs over the crabmeat. Cook over low-medium heat and wait for 30 seconds to allow the eggs to set around the edges.

Use a spatula to pull the set out edges of the eggs toward the center of the pan. Repeat around the pan to make sure all the eggs make it to the center of the pan. Keep turning over the eggs so that they cook all the way through. Swirl and twirl the eggs to break them up. When the eggs are about 95% cooked, remove them from the heat so they don't overcook. Sprinkle with chives and serve immediately.