Heat olive oil in a large skillet over medium heat, swirling oil to coat the skillet. Pour eggs into hot skillet; eggs will bubble and firm immediately.
Lift cooked edges of the omelet with a rubber spatula and tilt the skillet so that the uncooked egg runs underneath the lifted edge. Continue cooking, lifting edges and tilting the skillet, until omelet is almost completely set, 1 to 2 minutes total cooking time; remove from heat. Spread out any runny egg evenly on the top of the omelet with a rubber spatula.
Sprinkle goat cheese, 1 1/2 teaspoons chives, sea salt, and black pepper over omelet. Gently lift one edge and fold 1/3 of the omelet into the center over the cheese and chives. Fold the opposite 1/3 of the omelet into the center. Slide omelet to the edge of the skillet and flip, folded side down, onto a plate. Top with remaining chives.
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