Spread 2 teaspoons butter on bottom half of each croissant; place buttered-side up on baking sheet. Broil 5 to 7 inches from heat 1-2 minutes or until light golden brown.
Top each toasted croissant half with 1 slice cheese and 1/4 ham. Continue broiling 1-2 minutes or until cheese is melted.
Place 2 poached eggs and 1 slice cheese over ham on each croissant. Continue broiling 1 minute or until cheese is melted. Sprinkle with chives; top each with remaining croissant half.
To poach eggs heat 1 1/2 to 2 inches water in saucepan to boiling. Reduce heat to low. Break egg into small bowl; carefully slip egg into water. Cook until whites and yolks are firm, not runny. Remove with slotted spoon.