Preheat oven to 450 degrees.

Cut potatoes in half if small or into 1½ inch chunks and place in a roasting pan. Sprinkle on 2/3 of the salt and pepper and 2 tablespoons of the olive oil. Toss well to coat and arrange the potatoes in a single layer, cut side down. Roast for 20 minutes, flip the potatoes over and roast for another 10 minutes. Push the potatoes to the sides of the pan to make room for the fish. Pat the fish dry and sprinkle with the rest of the salt and pepper and drizzle on the remaining oil. Roast for 10 minutes or until the fish is opaque and just starting to flake.

While the potatoes are roasting, prepare the balsamic butter sauce. In a small saucepan over medium high heat, bring the balsamic vinegar and minced shallot to a boil and cook until it gets thick and syrupy (about 5 minutes). Take vinegar off the heat and whisk in 2 pieces of butter. Continue to whisk until the butter is melted and absorbed. Continue whisking in all the butter, 2 or 3 pieces at a time until it is all absorbed. The sauce will cool as you continue to whisk in the butter so work as fast as you can, making sure each addition of butter is completely absorbed before adding more.

Sprinkle the lemon zest and chives over the fish and serve the balsamic vinegar sauce on the side.