Place the potatoes in a large pot with enough salted water to cover and bring to a boil. Lower the heat and simmer until tender, about 15 minutes. Drain, return to the pot and toss with the parsley.
Meanwhile, in a large skillet, heat the olive oil over medium heat. Season the chicken breasts with salt and pepper and cook until browned, 5 to 8 minutes on each side; transfer to a plate.
Add the scallion whites to the skillet and cook, stirring, until softened, about 1 minute. Add the wine and grapefruit juice, scraping up any browned bits; bring to a boil and cook until reduced to 2 tablespoons, about 8 minutes. Remove from the heat and whisk in 1 piece of butter until smooth; repeat with the remaining 7 pieces. Stir in the grapefruit segments and scallion greens and season with salt and pepper. Serve over the chicken, alongside the potatoes.