Preheat the oven to 450 degrees F. On a rimmed baking sheet, toss the grapes and onion with the rosemary sprigs, balsamic vinegar, 2 teaspoons oil, 1/8 teaspoon salt and 1/4 teaspoon pepper. Roast, turning once halfway through, 20 to 25 minutes.
Meanwhile, cut the chicken breasts in half horizontally. Put a piece of chicken between 2 sheets of plastic wrap and pound with the smooth side of a mallet until the chicken is 1/4- to 1/2-inch thick. Repeat with the remaining pieces of chicken. Sprinkle all the chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper.
In a large nonstick skillet, heat the remaining 4 teaspoons oil over medium-high heat. Cook the chicken until golden-brown and cooked through, 3 to 4 minutes per side. Remove and keep warm.
Add the wine to the skillet; cook over high heat until reduced by three-quarters, about 2 minutes. Remove from the heat and let cool 1 minute. Add the butter and swirl until the butter is melted, about 30 seconds. Spoon the sauce onto 4 plates and add the chicken, then top with roasted grapes and red onions. Garnish with additional rosemary and serve immediately.