In a medium skillet, heat 1 tablespoon olive oil over medium-high heat. Add the onion and cook, stirring occasionally, until softened, about 5 minutes. Stir in the tomatoes, raisins, brown sugar, ginger, 3 tablespoons vinegar and 1/2 cup water. Bring to a boil, lower the heat and simmer until the sauce has thickened, about 10 minutes.
Meanwhile, season the pork with salt and pepper. In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Add the pork chops and cook, turning once, until browned and just cooked through, about 5 minutes.
In a pot of boiling water, cook the green beans until crisp-tender, about 3 minutes; drain. Transfer to a bowl and toss with the remaining 1 tablespoon olive oil and 1 teaspoon vinegar; season with salt and pepper. Top the pork chops with the tomato chutney and serve with the green beans.