Place the potatoes in a large pot with enough cold water to cover them by 2 inches. Add 2 teaspoons of the salt and bring to a boil. Reduce heat and simmer until almost fork-tender, about 15 minutes. Add the green beans and cook 5 minutes more, until just tender. Drain and set aside. In the same pot, melt the butter over low heat with the chives, 1/4 teaspoon of the salt, and 1/8 teaspoon of the pepper. Quarter the potatoes and return them to the pot with the green beans. Stir gently to combine. Season the fish with the remaining salt and pepper and place in a large skillet. Pour in just enough wine to reach halfway up the sides of the fish. Bring to a simmer over medium-low heat. Cook 6 to 8 minutes, covered, until the fish is opaque. Serve with the beans and potatoes. Spoon any extra chive butter on top of the fish.
Tip: You can replace the halibut with any firm-fleshed white fish, like swordfish. The fillets should be 1 inch thick.