For the fondue: Melt the butter over low heat in a saucepan. Stir in the flour and cook for 1-2 minutes until it starts to turn golden brown. Whisk in the milk until it starts to become thick and smooth. Remove from the heat and stir in the parmesan cheese and chives. Season with salt and pepper to taste. Cover with a lid to keep warm. Reheat on low if needed.
Fill a saucepan halfway with water. Bring the water to a simmer. Stir the vinegar into the water.
Crack the eggs into a bowl. Gently place the eggs into the water. (You can poach multiple eggs at once, being careful not to overcrowd the pan.)
Cook the eggs in the water for 3-5 minutes, gently flipping over about halfway through until the whites are firm. Remove the eggs with a slotted spoon onto a paper towel to drain excess water.
For the chicken sausage: If raw, cook in a 400°F oven to an internal temperature of 160°F using a thermometer. If already cooked: Preheat a non-stick pan over medium heat and brown the chicken sausage slices on each side.
Toast the English muffins.
Serve the eggs with chicken sausage and English muffins. Spoon the fondue over the eggs garnish with chives. Serve with oranges.