Toss the crab meat with the mayo, lemon juice, Old bay and Tabasco. Season with salt and pepper and stir in the fresh chives. Set aside.
In a bowl, whisk together the eggs and milk until smooth and slightly frothy. Season with salt and pepper.
Preheat an 8" skillet to medium heat. Melt 1 tbs butter and swirl around the pan until foamy. Add half of the beaten eggs to the pan. Drag a rubber spatula through the eggs to stir and break them up while still swirling to cover the pan. Cook for 2 to 3 minutes repeating this step until the omelet starts to hold. Add half of the crab filling and gently fold the omelet by sliding the pan off the heat and tilting on half towards you. Use some well honed spatula skills to gently fold the omelet as you roll in onto the plate.
Repeat with the remaining eggs and filling. Serve and bask in your breakfast making glory.